texts: In framing of audio samples', what is need of frame shift while giving frame size??

texts:
In framing of audio samples' in audio feature extraction, what is need of frame shift while giving frame size??
i.e. frame size  = 20ms,
     frame shift = 10ms.
Rather then shifting/overlapping why can't we use continuous frames then of overlapped??


texts:
Trying to understand whether or not I am calculating the PSD correctly. Below is the equation that I am using:

$$
PSD_{rms}(f_{m} = m \cdot f_{res}) = \frac{PS_{rms}
}{ENBW} = \frac{2 \cdot \left | y_{m} \right |^{2}}{f_{s}\cdot S_{2}} m = 0....N/2
$$

This equation is applied using the following:

1) Calculate the squared magnitude of the FFT bin:

$ mag = (re*re+im*im) $

2) For each of these magnitude, I calculate the following:

$ PSD(0...NFFT/2) = 2 \cdot (mag[0... NFFT/2] / Fs \cdot S2 $

So it looks like the following in code:

PSD[i] = 2 * (result[i]) / (12000 * S2);

I get the following result:

This looks like the result is being scaled correctly. However, the removal of the noise...

I have been told to use a band-pass filter, but, looking at the source code of Matlab in their spectrogram algorithm they do not pass the results through any kind of filtering algorithm.

My question is: Should the output be this, and, if so, should I therefore apply a filtering algorithm even though matlab does not?

Look at matlab result:


texts: convolution of two exponential signals with imaginary numbers

texts:
I can solve problems without imaginary numbers, but when exponential contain imaginary numbers, I can't solve the problem.
For example, $x(t)=e^{3jt}+e^{4jt}$, $y(t)=(e^{-3t}-e^{-4t})u(t)$ (where $j$ is imaginary number and $u(t)$ is step function) I can't calculate $x(t)*y(t)$ easily.
In other problem that I can handle, I just easily calculate the integrals and make the answers, but with these imaginary numbers on the exponentials, I can't calculate the integrals even with the help of the calculator
can somebody help me?


texts: Confused about how Echo filter diagram works

texts: The picture above is the block diagram of an echo filter. My question is, how does the delay, and gain block affect the output signal? I think that when the input signal is outputted with a delay from when the user and a smaller amplitude.


texts: Automatic Image Enhancement of Images of Scanned Documents (Auto Whitening)

texts:
Dropbox have make a blog post about there automatic enhancement method for scanned document image - Fast Document Rectification and Enhancement.

I followed the post and they mention a formula to make the enhancement:

J(x,y) = gain(x,y)*I(x,y) + offset(x,y)

Where $ J $ is the output image and I is the Input image, the problem is i don't understand how they calculate gain and offset for each pixel

Thank you for your reply

EDIT: add simple image


texts:
Is $y(t) = \cos(t) + x(t)$ a time-invariant system?

$y(t-k) = \cos(t-k) + x(t-k)$

But it isn't equal to $\cos(t) + x(t-k)$

So, would it be time-invariant?


texts:
Was recommended to migrate this question from SO.

I am building an iOS app that, as a key feature, incorporates image matching. The problem is the images I need to recognize are small orienteering 10x10 plaques with simple large text on them. They can be quite reflective and will be outside(so the light conditions will be variable). Sample image http://i1274.photobucket.com/albums/y425/Chris_Mitchelmore/2_zpsce84d4f3.png

There will be up to 15 of these types of image in the pool and really all I need to detect is the text, in order to log where the user has been.

The problem I am facing is that with the image matching software I have tried, aurasma and slightly more successfully arlabs, they can't distinguish between them as they are primarily built to work with detailed images.

I need to accurately detect which plaque is being scanned and have considered using gps to refine the selection but the only reliable way I have found is to get the user to manually enter the text. One of the key attractions we have based the product around is being able to detect these images that are already in place and not have to set up any additional material.

Can anyone suggest a piece of software that would work(as is iOS friendly) or a method of detection that would be effective and interactive/pleasing for the user.

Sample environment:
http://www.orienteeringcoach.com/wp-content/uploads/2012/08/startfinishscp.jpeg

The environment can change substantially, basically anywhere a plaque could be positioned they are; fences, walls, and posts in either wooded or open areas, but overwhelmingly outdoors.


texts: In Matlab: how do I quickly create smoothing matrices?

texts:
Say I have 5 measurements of a signal as a column vector: x.
I can smooth the signal by multiplying it with a smoothing matrix:

$\ \mathbf{xs=S*x} $

For instance I might use [1 2 1] as a smoothing kernel in which case I get:

S =
     2     1     0     0     0
     1     2     1     0     0
     0     1     2     1     0
     0     0     1     2     1
     0     0     0     1     2

So far I have been using the function sparse() to build the matrix diagonal by diagonal,
but this quickly becomes tedious.

How can I quickly create a mxm smoothing matrix from a 1xn convolution kernel in Matlab?


texts:
I am searching for a matrix definition for converting a audio signal (5.1 with rear) to a audio signal (5.1 with side).
Currently I am using the definitions from: https://msdn.microsoft.com/en-us/library/windows/desktop/ff819070(v=vs.85).aspx.
But I am missing the yellow marked matrices:

Does anybody has got an idea where to get it from?
EDIT: Would be perfect if someone would have some other matrices else like quadrophonic,...


texts: How to calculate the output image with the following kernel?

texts: What is the advantage of using this equation? I guess we may use Taylor series, but  I tried my best and could not get   the equation.


texts: RMS from calculation from PSD using Welch's method

texts:
I've used Welche's method on a vibration signal to get the averaged FFT which I want to used to calculate the PSD from which I can calculate the RMS.

Within the Welche method i've use Hann window with zero overlapping. The following post states, that using
windowing couses distortion in the energy, which has effect on the RMS:
https://community.sw.siemens.com/s/article/window-correction-factors .

However not using windowing might lead to spectral leakege.

My question is, that what is the correct way of dealing with this problem? Shall I use uniform windowing, or shall I use correction factors on the FFT?


texts: Time and frequency domain spreading in CDMA and MC-CDMA?

texts:
For time domain CDMA transmitter, how the spreading sequences should look like? Is it necessary to be from $\{ -1,+1\}$ like PN sequences ? How will the codes be in frequency domain?
I am confused in spreading codes used for MC-CDMA and CDMA.
If I use a PN sequence $\in \{ -1,+1\}$ and then take FFT, it is MC-CDMA.
Now, If I directly use a DFT matrix as spreading codes, is it equivalent to MC-CDMA?


texts:
I have this little doubt regarding how to draw a block diagram representation of a difference equation. Let us implement $ y(n) = ay(n-3) + by(n-2)+cy(n-1) + x(n)$ in block diagram where $a, b, c$ are constants. What I made is this.

Is this block diagram wrong? They say that you should use only $z^{-1}$ delay multiple times to produce the effect of $z^{-3}$ and $z^{-2}$. But I think that this diagram is also correct. Please help.


texts: Feature recognition within a single song

texts:
I want to write an algorithm in C++ which is capable of identifying specific features within a single song, e. g. the sound of a drum which is played 100 times during 5 min.

State of the project

So the first thing I did was to import my *.wav-file, perfrom a step-wise FFT of the signal in order to create a time-frequency-pattern as shown in the figure below (x-axis: frequency, y-axis: time [ms], color: magnitude [dB]).

Here you can see the magnitude of a single frequency over time:

In the second picture one can easily see, that the pattern of the drum stays the same and is only shifted in time (peaks).

If I would only have this single song, it would be straightforward: I could search for points reaching a specific dB value and read out the corresponding time. However, I want to apply this algorithm to many different song files and don't want to manually adapt the values each time.

Problem

Which method could I use to identify such features? I thought about pattern recognition by neural networks, but I am not sure if this is the most appropriate solution.

I already read wikipedias article about pattern recognition (I am not allowed to make more than two links, sorry for that) basically saying that there are many different algorithm, but I think I need some help selecting the most appropriate one for my problem.

Edit 1:

My current approach is to use blob detection in order to read out different areas like the bass features and feed the blobs and their properties to a Neural Network in order to categorize them.

Thank you in advance!

Cheers, Urs

Links Sorry for the missing http://, i am not allowed to post more than two links

t-f-relationsip of music in general: ecee.colorado.edu/~mathys/ecen1200/sound/sounds2006_6pp.pdf

time frequency analysis of music: en.wikipedia.org/wiki/Time–frequency_analysis_for_music_signals

perhaps helpful: en.wikipedia.org/wiki/Harmonic_pitch_class_profiles

might be helpful, but I don't understand it: resources.mpi-inf.mpg.de/departments/d4/teaching/ss2009/mp_mm/2009_MuellerMeinard_Lecture_MusicProcessing_AudioStructure_handouts.pdf


texts: Is there any algorithm to decompose a wave into a set of given frequencies?

texts:
I heard about Fast Fourier Transform can decompose any waves.

But it seems like it was hitting for "all frequencies", namely, n HAVE TO be from 0 to N-1!

What if I want to decompose the wave into the frequencies I want!?

Such as, for example, 5Hz, 14Hz, 37Hz, 42Hz, 59Hz, etc.!?

Is there any algorithm that could do the job!?

PS. My understanding of FFT is from Google, and the degree of understanding is VERY limited! So PLEASE forgive me for my lack of knowledge and any stupid comments!


texts: How to determine if a filter is bandpass/stopband from its pole-zero diagram in z-domain

texts:
How can we determine if a filter is bandpass or stopband, just by looking at its pole-zero diagram in z-domain?

For exmaple, if we have a system with third-order pole at the origin and a zero on the real axis at 0.5, what is the type of this filter?

In general, what is the effect of zeros outside the unit circle on frequency response magnitude?


texts: How to derive the stationary Kalman filter predictor?

texts:
In its chapter on Kalman filters, my DSP book states, seemingly out of the blue, that the stationary Kalman filter for a system

$$\begin{cases} x(t+1) &= Ax(t) + w(t) \\
y(t) &= Cx(t) + v(t)
\end{cases}$$

has the predictor

$$\hat{x}(t+1|t) = (A-A\bar{K}C)\hat{x}(t|t-1) + A\bar{K}y(t)$$

and stationary state vector covariance and Kalman gain

$$\bar{P} = A\bar{P}A^T - A\bar{P}C^T ( C\bar{P}C^T + R )^{-1}C\bar{P}A^T + Q$$
$$\bar{K} = \bar{P}C^T(C\bar{P}C^T+R)^{-1}$$

where $Q$ and $R$ denote the covariances of the input noise $w$ and measurement noise $v$, respectively.

I can't see how to arrive at this from the minimum variance predictor. Could someone explain it to me, or point me to a resource that derives the expression? This is the time-variant minimum-variance filter, which I can derive:

$$\hat{x}(t+1|t) = (A-K(t)C)\hat{x}(t|t-1) + K(t)y(t)$$
$$P(t+1|t) = A\left(P(t|t-1)-P(t|t-1)C^T(CP(t|t-1)C^T + R)^{-1}CP(t|t-1)\right)A^T+Q$$
$$K(t) = AP(t|t-1)C^T(CP(t|t-1)C^T+R)^{-1}$$

I'm just unsure about how to go from here to the stationary filter above.

Update: I can see that substituting $\bar{P} = P(t+1|t) = P(t|t-1)$ and $K(t)=A\bar{K}$ into the time-variant filter results in the stationary filter, but why multiply with $A$? Is this just a symptom of an unfortunate choice of notation, meaning that either $K$ or $\bar{K}$ doesn't really denote the Kalman gain?


texts:
I program function to calculate the overlap area between 2 images (which is called fixed and floating) after transformation but it takes much time and it's complex for me to combine more than one transformation parameter together.

In Matlab, the built in functions affine2d can make affine transformation (rotation, translation, and scaling) that can solve my problem. However, this function depends on imwarp which fills the empty space with new pixel (default: black).

As you can see the below image, my ROI inside the red box in the both images.

How can extract this area from the transformed image (float)?

Update: the hardest part is to find the ROI coordinator in the transformed image.


texts: Logarithmic Amplitude Spectral Subtraction

texts:
I'm diving into audio processing and I'm trying to wrap my head around spectral subtraction. I learned there are different approaches do it based on power, magnitude, oversubtraction. My task is to perform the spectral subtraction based on the logarithmic amplitude.
My question here is:
What is the difference between magnitude spectral subtraction, logarithmic amplitude spectral subtraction, and oversubtraction?
My second question:
Which method would be more efficient for feature extraction in the context of irregular speech (noise, silence, mispronunciation...etc)
Formulae
Magnitude spectral subtraction: $\ |\hat{X}_m( \omega )| = max\{|Y_m( \omega )| -  E[|D_m( \omega )|],0\}$
Power spectral subtraction: $\ |\hat{X}_m( \omega )|^{2} =  max\{|Y_m( \omega )|^{2} -  E[|D_m( \omega )|^{2}],0\}$
Oversubtraction: $\ |\hat{X}_m( \omega )|^{2} =  max\{|Y_m( \omega )|^{2} -   \alpha E[|D_m( \omega )|^{2}], \beta[|D_m( \omega )|^{2}] \}$
Source link
I couldn't find the formula for the logarithmic amplitude spectral subtraction.
Thank you all and happy, and healthy new year.


texts: Where does convolution fit into tracking fluorescent photons using MC models?

texts:
I have been reading this old paper by Steven Jacques, a titan in the world of using Monte-Carlo methods for photon propagation and distributions.

https://www.osapublishing.org/ao/abstract.cfm?uri=ao-28-20-4286

For the moment, I have a pretty solid grasp how to continue with my research. However, there is one element that has me perplexed. The author states this powerful formula:

$$
F(\lambda,r) = \int_0^D\int_0^{2\pi}\int_0^\infty \psi(r',z')\beta(\lambda,z) \circledast E(\lambda,\sqrt(r^2+r'^2-2rr'cos\theta')
$$
Which shows up again and again in more recent papers.
https://www.ncbi.nlm.nih.gov/pubmed/9203387

https://www.ncbi.nlm.nih.gov/pubmed/24307289

https://www.ncbi.nlm.nih.gov/pubmed/21945055

And it seems to work well enough to last the ages, so I would like to implement it myself. However, I get confused by the convolution operator presented above. $\psi$ is just in terms of the depth of the laser and corresponds to the excitation laser being launched. This has spatial dependence hence r and z. So we can approximate this as a 3D matrix. $\beta$ is by the layer, so it depends on how many layers we want to simulate. In skin, we could  have 4 layers. E is the escape function, which means how many photons reach the surface of the medium when launched isotropically from a depth in the medium. E and $\beta$ also depend on the wavelength and are experimentally validated. My BIG question, though, is how to do the convolution to both  sides, and what would that actually represent.

We summarize, we have $\psi$ as a 3D matrix, $\beta$ as a vector of equivalent depth and E as a 3D matrix the same size as $\psi$.


texts: Training and testing set for speech recognition

texts:
I am the moment looking for a dataset similar to the caltech 101, but in this case for different phrases, words and so on... In general just words.

Does someone know if such dataset exist, or I have to create it myself...


texts: Question About Linear and Circular Convolution - 1D and 2D

texts:
We know that applying a filter on an image is called correlation or convolution depending on the filter angle. In Gonzalez I have read that we can apply linear convolution on an image. Here I have a doubt.

Suppose we have a vector image of 4 elements and a filter/kernel also of 4 elements then we get the output of linear convolution which contains 7 elements (4+4-1). Does that mean now the image is represented by 7 elements? If not then what does these 7 elements represent?
Also I want to know where do we use Circular Convolution. I have read many posts but not able to get it fully.
Last question is from filtering in frequency domain. We know that convolution of f(x,y)* h(x,y) in the spatial domain is equal to the product of DFT's of the image and the kernel i.e F(u,v).H(u,v) in the frequency domain. Then if we have a 64 *64 image and 3*3 filter, please tell me what will be the size of the sequence obtained by applying Linear Convolution in the spatial domain. Also Do we take the DFT of the image f(x,y) as it is or do we need to pad the image first before taking its DFT and if padding is needed how much? I know filter size should also be 64 * 64, so we need to change filter size from 3 * 3 to 64 * 64. It means padding of 61 rows and 61 columns of 0's but where should we pad these 0's. These 0's cannot be equally divided top,bottom,left , right as 61 * 61 is an odd number. Please explain.


texts: help to calculate phase shift in certain frequency(identified from FFT)

texts: I am designing a 24ghz doppler radar, with 1TX 2RX. Four adc channel are recording at 25khz, applying 256point FFT on adc of both of RX I and Q, I could identify the target in certain doppler frequency(speed) . The next step is to calculate the phase shift to get the angle of the target, that's where I stuck. Since I locate the target on FFT, how to trace it back to the time domain and calculate the phase shift between the different RXs. Any input will be very welcomed. I am a computer engineer with limited knowledge of dsp though, but facinated about radar.


texts: Using phase information to extract sample values

texts:
I have one cycle of the following signal stored in a memory:

 x(n)=sin(2 * pi * n/N + theta)

 where  theta= 2*pi*q/N and q, N are integers.

How do I use these values to obtain sinusoides (samples) with same frequency but different phase?


texts: How to implement the imaginary part of FFT equation applied to a signal in computer/C++?

texts:
I am trying to apply FFT on a time domain signal in C++, however I am having trouble with the imaginary part i.e square root of -1. In the FFT equation we have,

$$X =\frac{1}{2\pi}\int_a^b x(t) \ e^{-j\omega t} \ dt$$

we know that:
$$
e^{-j\omega t} = \cos(\omega t) - j\sin(\omega t) \tag{2}
$$

we also know that:

$$ \ j = \sqrt{-1}\ $$

Problem :  I am trying to apply the fft equation on a signal and the problem of implementation arises when coding the equation(2) in C++. As, we know the value of $ \ j = \sqrt{-1}\ $ is infinite or if tried to solve using a calculator, we get a Math Error*. And so is my program giving an error and I'd like to get suggestions and advises on how to solve this issue and apply the FFT equation in C++.


texts: Mathematics behind the creation of 3d face mask at runtime

texts:
I'm new in Image processing and Machine learning area. I want to create 3d mask of face at runtime.
import numpy as np
import dlib

cap = cv2.VideoCapture(0)

detector = dlib.get_frontal_face_detector()
predictor = dlib.shape_predictor("shape_predictor_68_face_landmarks.dat")

while True:
    _, frame = cap.read()
    gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)

    faces = detector(gray)
    for face in faces:
        x1 = face.left()
        y1 = face.top()
        x2 = face.right()
        y2 = face.bottom()

        landmarks = predictor(gray, face)

        for n in range(0, 68):
            x = landmarks.part(n).x
            y = landmarks.part(n).y
            cv2.circle(frame, (x, y), 3, (255, 0, 0), -1)

    cv2.imshow("Frame", frame)

    key = cv2.waitKey(1)
    if key == 27:
        break

I find mention code online, which find 68 point on face.
I want to know the Mathematics behind it. All I know that partial differentiation is used but I can't understand how. Also Some details about how to create 3d face mask at runtime will be appreciated.


texts: Visual Tracking / Object Tracking: Estimate the Direction the Whale Is Moving

texts:
I am trying to find out which way the whale is moving. So I have an image of the whale swimming in the water and I want to find out where is it located and which direction does it swim (with respect to X/Y coordinates of the image).

For example here the angle is approximately 30 degrees in respect to X coordinate.

So my idea was to use canny edge detection to extract edges, construct a matrix from the points of the edges, calculate SVD and use the U matrix from SVD as a rotation matrix to get the angle.

So I have done something like this in python:

Where the first image is the starting image, the second one is the edges, and the third one is the scatterplot with points from the edges and the red arrow is a direction of the angle I got from the SVD. The angles I got

Angle 146.73
Angle 135.08

are not even close to real angles (which are approximately 30 and 85 degrees).

I have tested that I get a correct angle when I SVD the gaussian matrix, which I rotated by some degree.

This is my first post, so if you need some clarifications (code that I used, explanation why I think this approach will work or anything else), please let me know.

So am I on the right track to find where the whale is going (and just made some silly mistake) or should I use another idea?


texts: How to get a real signal from complex ifft values?

texts:
I am trying to understand the difference between DCT and FFT in the context of compression. There is a nice practical example given here. (near the end of the page)

When I try it in matlab I am stuck at plotting the ifft values (which are complex). The plot command cannot plot the complex signal. One natural question comes to my mind, when is the ifft value complex, and when is it real? If it is complex, is it fine to discard the imaginary parts and keep only the real part?

What is the right way to reconstruct the real signal x from ifft complex values?


texts: Why the bandwidth of the system with the minimum-order observer is higher than the full-order observer?

texts:
In Ogata's Modern Control Engineering (5th Ed., page 786) it says:

  The bandwidth of the system with the minimum-order observer is higher
  than that of the system with the full-order observer, provided that
  the multiple observer poles are placed at the same place for both
  observers.

Can anyone explain me why this is so?


texts: Zernike Moments' implementation in OpenCV

texts:
The reason why Hu moments were implemented in OpenCV and why Zernike moments were not implemented is looking like their performance similar as stated in this paper.

As stated in the paper Zernike moments' advantage is their reconstruction facility.

If there is a reliable implementation of Zernike moments compatible with OpenCV I would like to test their shape matching performance with OpenCV's Hu moments shape matching performance and if possible reconstruction facility.

Thanks.


texts: Robust peak detection taylored for spectroscopy

texts:
i need a algorithm for peak detection in raman spectroscopy. I tried this one, but it did not give me satisfying results.

Spectrums may look like this:

In professional software, i think they use the fact that the peaks can be fitted as lorentz-Peaks.

However i don't really know how to start with it. I think i would still need some way to detect the peaks itself, so i can fit to it? What i need then is a function where i give the spectrum as input (so a list of ($x$|$y$) tuples) and get the center and half-width of each peak. It should be robust against noise, but still detect shoulder-peaks, so small peaks which are overlapping into a stronger peak.

Ideally, i don't want to dig too deep into signal processing theories, but i suspect i might have to.

If possible, it should detect lorentz-shaped or gaussian-shaped peaks even when the $y$-axis is nonlinear "distorted". Meaning there is a correlation between the measured $y$-values in pixels, and the true values in $cm^{-1}$, which is not linear, but some quadratic or even cubic relation, which will not always be known.


texts: Kalman Filter with Accelerometer with DC Offset

texts:
Goal: For a particle moving uniaxially, to estimate position ($d$) and velocity ($v$) from noisy acceleration ($a$) and very noisy position (GPS) measurements using a Kalman filter.

Catch: The accelerometer has a DC offset, i.e. its zero is not zero but some number $\Omega$ such that the "true" acceleration $a^{true}$ is obtained from the measured acceleration coming out of the sensor $a^{obs}$ as:
$$
a^{true}=a^{obs}-\Omega
$$
My system states and transitions, note I've added the accelerometer bias or DC offset as a state are:

$$
\hat{x}_{k+1}=\left[\begin{array}{cccc}
d_{k+1} \\
v_{k+1} \\
a_{k+1}^{true} \\
\Omega
\end{array}\right]=\left[\begin{array}{cccc}
1 & dt & dt^2/2 & 0       \\
0 & 1 & dt & 0       \\
0 & 0 & 1 & 0       \\
0 & 0 & 0 & 1
\end{array}\right]\cdot\left[\begin{array}{cccc}
d_k \\
v_k \\
a_k^{true} \\
\Omega
\end{array}\right]
$$

And then the measurements are (notice I've used $a^{obs}$ instead of $a^{true}$):
$$
z_k=\left[\begin{array}{cccc}
1 & 0 & 0 & 0       \\
0 & 0 & 0 & 0       \\
0 & 0 & 1 & -1       \\
0 & 0 & 0 & 0
\end{array}\right]\cdot\left[\begin{array}{cccc}
d_k \\
0 \\
a_k^{obs} \\
0
\end{array}\right]
$$

Question 1: Does this look right and/or feasible and,

Question 2: How do I determine the process noise and measurement noise matrices $Q$ and $R$?

Thanks for your help.


texts: Accelerometer Inference from power spectrum

texts:
I have 3d accelerometer data sampled as 60hz. When I am looking at the power spectrum in all three accelerations (x,y,z). I am noticing a trend with a negative slope. I trying to figure a few things out:

What could the cause of this trend be? System bias or something else?
Best way of handling this - Matlabs detrend tool does not have much of an effect. What would be the best way to correct this?


texts: Open Source Implementation of 3D Thinning algorithm

texts:
I am looking for open source implementation of thinning algorithm in 3D.

  Thinning algorithm: Convert binary shapes to 1-pixel wide lines, without shortening it or breaking it apart. For example, the thresholded version of hand written or printed alphanumerics can be thinned for better represetation and further processing.

This particular thinning algorithm I am looking for does not disconnect an object or split an object up into multiple parts. Moreover, it does not shorten the shape.

Are there such source codes available? If 3D is not available, 2D is fine too. I can take it from there.

UPDATE:

Somebody has requested me to elaborate on what am I after. Here:  http://www.mip.sdu.dk/ipl98/how_to_use_ipl98/tutorial/node52.html There are several images in the link here on thinning and skeletonization. I can see that thinned algorithm and skeletonization algorithm produce similar yet different result. But what I am after is to have all shapes in a binary image to become thinned without shortening the shape. To clarify things further, here is what I wanted:

This is original image:

This is skeleton image:

This is thinned image:

As you can see, skeleton image and thinned image have different results. Thinned image has lesser lines and produce an outline that looks more like the thinned original. But these images are in 2D, I am looking for an algorithm to do thinned binary image in 3D.


texts: What do I need to know to difference a note for different musical instruments? for example, if they play the same note, (same frequency), how can I difference them if they have the same frequency?


texts: Prove a property using shift theorem and duality

texts:
I'm reading Lectures on the Fourier Transform and Its Applications and I'm going to prove shift theorem for the inverse Fourier transform using duality. According to the mentioned source, the duality equations are
$$\mathcal{F}f = (\mathcal{F}^{-1}f)^{-} \tag{1}$$
$$\mathcal{F}f^- = \mathcal{F}^{-1}f \tag{2} $$
$$ \mathcal{F}\mathcal{F}f = f^{-} \tag{3}$$
Where $$(\mathcal{F}f)(s) = \int_{-\infty}^{+\infty}e^{-2\pi i st}f(t)dt$$ $$(\mathcal{F}^{-1}f)(t) = \int_{-\infty}^{+\infty}e^{+2\pi i st}f(s)ds$$
And $$f^{-}(t) = f(-t)$$
Using shift theorem which says $$f(t) \leftrightarrow F(s) \implies f(t-b) \leftrightarrow e^{-2\pi isb}F(s) \tag{4}$$ And duality equations I want to show $$F(s) \leftrightarrow f(t) \implies F(s-b) \leftrightarrow e^{2\pi itb}f(t) \tag{5}$$
First of all $\text{(5)}$ seems ambiguous to me but I guess it's $$\mathcal{F}\{ e^{2\pi itb}f(t)\} = F(s - b) \tag{6}$$
It's straightforward to show that directly $$\mathcal{F}\{ e^{2\pi itb}f(t)\} = \int_{-\infty}^{+\infty}e^{-2\pi i st}e^{2\pi itb}f(t)dt = \int_{-\infty}^{+\infty}e^{-2\pi it(s-b)}f(t)dt = F(s-b)$$
But I don't know how to combine duality equations and shift theorem to prove $\text{(5)}$. There is another version of duality which can be found for example here. It says $$x(t) \leftrightarrow X(s) \implies X(t) \leftrightarrow x(-s) \tag{7}$$
Is $\text{(7)}$ same as duality equations i.e. equations $\text{(1)}, \text{(2)}$ and $\text{(3)}$ or they are different from each other?
Edit: Equation $\text{(6)}$ is called modulation theorem. Also it seems in $\text{(5)}$ by $F$ we mean $\mathcal{F}^{-1} f$. So it's completely different from $\text{(6)}$. I'm really confused by these similar equations.
Edit2: I realized that the other version of duality is same as $\text{(3)}$. I mean the equations $\text{(3)}$ and $\text{(7)}$ are identical.


texts: What does this block do? It's part of a block diagram for a RMS/Peak detector.


texts: Finding optimal decision threshold for binary comm system

texts:
I'm trying to solve the following exercise: Given a system that transmits bit $b$ with probability $p_b$ and $-b$ with $p_{-b}$ and the transmission is degraded by AWGN $N(0,\sigma^2)$. What is the optimal decision threshold $\mu$ to minimize the probability of error? Use Q functions to express the probability of error.
My approach:
$P_e = P_b P(-b|b) + P_{-b} P(b|-b)$, where $P(-b|b)$ means probability of detecting $-b$ given that $b$ was transmitted.
$P(-b|b)$ is the left tail of the distribution ($\Phi$) since I need to receive a value smaller than $\mu$ after sending $b$, but since the exercise asks in $Q$ -> $Q(-(\frac{\mu-b}{\sigma}))$
$P(b|-b)$ is already the right tail as I need to get something greater than $\mu$ after sending $-b$, so $Q(\frac{\mu+b}{\sigma})$.
To find the optimal $\mu$, I took the derivate of $P_e$ with respect to $\mu$ and set it equal to 0.
To facilitate notation, I will use $X = \frac{-(\mu-b)}{\sigma}$ and $Y = \frac{\mu+b}{\sigma}$.
Now I have $P_1 e^{-\frac{X^2}{2}} = -P_{-1} e^{-\frac{Y^2}{2}}$.
After some manipulation and taking $ln$ on both sides: $ln(\frac{p_1}{p_{-1}}) = \frac{\frac{Y^2}{2}}{\frac{-X^2}{2}} = \frac{2\mu b}{\sigma^2}$.
So, $\mu = ln(\frac{p_1}{p_{-1}}) \frac{\sigma^2}{2b}$ but the solutions I have don't have the $\sigma^2$ term, so I cannot find where I made a mistake.
As for the derivative of the $Q$ function, it should be $-\Phi'$, right? Which ends up being the pdf, so $e^{-\frac{z^2}{2}}$ (omitting the normalization factor as they will cancel out on this particular question)


texts:
DVB-T2, 32K SISO, not extended.

I've acquired P2 symbol, PRBS bits have matched with bits recovered from pilots. Then equalization was applied to all subcarriers. The constellation I've got looks exactly like rotated 16-QAM overlapped with non-rotated 64-QAM.
On the picture: the red dots(-1,0) and (1,0) are for pilots, the blue dots for everything else, except tone reservation.

DVB-T2 Implementation guidelines (ETSI TS 102 831 V1.2.1 (2012-08)) clearly states:

  Constellation rotation shall only be used for the common PLPs and the data PLPs and never for the cells of the L1
  signalling.

What do I miss?
Also, can't find if there any subcarriers (cells) inverleaving applied to P2 symbol, can anyone explain this?


texts: What fps can be considered as a hardline for real-time performance? Is there any academic paper that describes this?

texts: I am trying to design a deep learning based inferencing solution for security applications. My deployed program achieves an FPS of 15fps for classification. Can it be considered real-time?


texts:
I am doing a Fourier decomposition of sea level series ( to find out one particular contribution within the sea level height). it should be applied subsequently on shifted (by one hour) windows of 96 hours length.
I have already the a, b as the following:

where x is the sea level series (hourly dataset)

As a start I tried to code only the first time window as the following code to simplify the coding because I am just a beginner in Matlab but unfortunately I am getting wrong results as the amplitude is higher than the actual sea level
here is my code so far

`hour_window = 96 ;
T= 19,8 ;
f = 1 / T ;
% sea_level is a vector of the first 96 values ( as I am doing only the first interval)

for j = 0: hour_window -1
a = sealevel .* cos(2*pifj) ./ cos(2*pifj).^2  ;
b= sealevel .* sin(2*pifj) ./ sin(2*pifj).^2  ;
 end
A = sqrt(a.^2 + b^.2) ;
phase= atan2(a,b) ;`

I would really appreciate any help
thanks in advanced


texts: How do I go about detecting whistles, pops and other sounds in live audio input?

texts:
I've read many questions on SO, and frankly, each one of them is not describing any particular way to go about it. Some say "do FFT" and some say "zero crossing" etc. But I've only gone as far as understanding that the digital audio input consists of an array of amplitudes for a particular frequency and well.. Don't really know much beyond it.

Now I do know Nyquist theorem, frequency, amplitude, Fourier series etc, and that's from 2-3 years ago when I did that in my university program in some semester. But back then we really weren't taught the real world usage of Fourier much, and I didn't bother to dig up more on the subject beyond learning just enough to pass the subject. But now I'm gonna have to use all that stuff.

Here's a snapshot of the sounds I'm trying to detect:

Clearly the sounds have unique graphs. I just want to understand how to extract their particular unique characteristics for their unique spiky lines in the graph. Like what amplitude, frequency, etc. And for how much time - although that is trivial I guess.

I want a simple step by step, un-vague instruction list - I can google the terminology I won't understand.

Like perhaps this? --

Get input audio data
Plot spectogram
Get spectogram graph for the sound you want to detect in a noiseless environment
Study that graph - draw unique characteristics of that sound
Make some kind of function that can detect those particular characteristics in live audio feed, using the characteristics of the sound found in (4)
If a match is found, well - the job's done.
Polish the algorithm to weed out false negatives.

Where I am confused is - how do I go about 3,4,5. Particularly 3 and 4.
Because I'm making a software where in the user would be able to record any sound as a gesture input to be used later, I would want my system to be able to record any sound and match it against live audio feed to detect that sound gesture. Like say, coughing, or finger snapping, or whistling, or clapping. Or saying consonants - $A$ or $B$ or $X$ or $Z$. Just about any sound.

I was thinking of making the user record the sound they want to store as a gesture in a quite environment. And the user would make the sound only in between the quiet time padding; 3 secs in the beginning and in the end of the recording.

So say, during the first 3 secs, my system would establish that the current input is the normal quiet background sound. And then a sudden change in the graph would be the sound input starting. And when that stops, the recording would go on for another 3 secs, the trailing quiet time padding. This would be done manually by the user. It would then automatically store the characteristics of only that part during which the sudden change in the graph lasted - somewhere between the padding times.

And thus the characteristics of that part would be saved as that sound's gesture data, which would be used to detect that particular sound in live audio feed later on.

Problem is, that I'm thinking all this in plain English. I need to think in maths and physics, to be able to implement it efficiently in my code. I'm just so damn clueless about what to write and where to write it in my code - even with so many libraries and questions on SO at my disposal.

And sorry if this was long.


texts:
I want to determine the frequency response of a filter bank
from the input x[n] to the four output channels.

$H_0$ is an lowpass and $H_1$ is a highpass filter.
Both are FIR filters and I have the numerator coefficients of them,
they have an order of 50.

My attempt in matlab would be to use the downsample command on the filter coefficients and multiply them element-wise and pass the result to the freqz command.

So from $x[n]$ to $x_4[n]$ I'd do it the following way:

freqz(downsample(num_h0, 2) .* downsample(num_h0, 2) .* downsample(num_h0, 2));

Is this the right way or am I missing some point here?

Also how do I plot all four frequency responses in one plot,
respectively how do I have to scale the frequency axis?
Is it right to say that the sample rate of $x_4[n]$ is
$\frac{1}{8}$ of the inputs sample rate.


texts: How to Enhance the height difference of the experimental signal data?

texts:
I'm very new to signal processing. Is there any kind of method to enhance the signal of experimental data that I get from the experiment? Especially on the difference of y-axis. Thank you

This signal is coming from the surface plasmon resonance experiment using gold colloidal to immobilize the gold thin layer, the Y-Axis is the intensity of how the signal response to the refraction index change and the "SIGNAL" measured by intensity differences and the X-Axis is time, so right now my signal response is pretty weak and recently my Professor ask me can I tried to enhance my weak signal without changing the experimental input or procedure.


texts: How can one put information within a signal waveform and make it to traverse through different kind of medium?

texts:
This is a soft question. There are different types of signals
like analog ,discrete or digital one.

But my question is how can one put information within a signal waveform and make it to traverse through different kind of physical medium, electronic circuits,devices etc?

Moreover ,in physics,we have Newtons laws for conservation of mass and energy . Now,is there any similar law in case of signals?


texts:
I am writing a report, and my advisor asked me to explain why I scale the fft by a factor 1/N (where N is the length of the array).

I used to use the scaling convention of multipling the fft by the time increment (dt), this convention was good for me, because it ensures the check of the Parseval theorem. Unfortunately I had discussion with one of my advisors, because, since this convention does not give you the right amplitude, he thinks it is wrong. As I have read online, there are not right convention or wrong convention. If I use the factor 1/N the amplitude is checked, if I use the factor dt then the parseval identity is preserved.
I have 2 question now:

Why, doing the fft, I cannot have both: amplitude checked and energy checked?
I have already demonstrated (in my report) that if I scale the fft by a factor 1/N, I obtain the right amplitude, since the first value of my fft is equal to the time average of my function. Now I would like to show with formulas why this convention gives me the right amplitude? I have already searched online and here on the forum, but I did not find any good answer that explain every passage.


texts: Subcarrier assignment in MIMO-OFDMA system

texts: Is it possible for multiple users to simultaneously transmit on the same subcarrier in a MIMO-OFDMA system?


texts:
In this link on page 218, just before the first paragraph ends, it says:
" We can interpret the power axes as one-half the square [...] of the modulus of the complex envelope."

In the same paragraph, the average input power is stated to be $P_\text{in} = A^2/2$. Can somebody please explain to me, why there is no resistance ?
The amplitude probably refers to a voltage signal. The RMS of a sinusoidal signal is $A/\sqrt(2)$. Since this is the square root of the mean, it makes sense to me, that the average input poewr is $A^2/2$. But still, I am confused about the lacking resistance. Especially, since in the second paragraph, it is stated, that the power axis will be graduated in units of $10\log(P_\text{in})$.


texts: How would you put this "IIR Approximation of FIR Filters Via Discrete-Time Vector Fitting" into Matlab?

texts:
https://www.eee.hku.hk/~culei/publication/ISCAS-0590.pdf

This paper talks about a way to approximate FIR filters using IIR via a method known as Discrete-Time Vector Fitting. I am confused on how I would implement this into Matlab.
Can anyone help me?


texts:
I am dealing with the transfer function of an FIR filter:

  $$H(z) = (1-0.5z^{-1})(1-2z^{-1})$$

I am having trouble determining which type of Linear-phase FIR filter it is, Type 1-4. I believe it may be Type 2, but not certain.

Also I need to determine the frequency response of the filter. Is it just as simple as replacing the $z^{-1}$ terms with $e^{-j\omega}$ in order to get the frequency response? If so this results in frequency response of

  $$H(e^{j\omega})=e^{-j\omega}(-2.5 + 2\cos(\omega))$$

And I am not sure how to take the magnitude or phase of that frequency response, any help would be greatly appreciated.


texts: How multi layer map to different beams in LTE Beamforming

texts:
I understand for SU-MIMO Beamforming single layer maps to all antennas with phase shift applied to create beam. Also I understand in this case all beams will be carrying same signal (say s1).
But in case of MU-MIMO how can s1 and s2 be transmitted from multiple antennas at the same time so that one of the resulting beam carries s1 and other carries s2?


texts: Determining sampling rate in OFDM demodulation

texts: I have seen that in OFDM, the sampling rate is much lesser than twice the bandwidth of signal. why is it so? How is sampling rate calculated in OFDM? Does it depend on the modulation type used inside like QAM or BPSK. Does it relate to FFT length by any chance.


texts: Finding a good inverse for an ill-conditioned matrix transformation

texts:
I have a time-series observation dataset that has been distorted. I want to recover the best approximation of the original signal as possible. Disclaimer:: I know only the basics of linear algebra, so please bear with me.

I have a good model of the distortion, represented by a square matrix. In theory, if I can find an inverse of the transformation, I can recover the original signal. However, the model of the distortion as a matrix is ill-conditioned (i.e. almost singular).

Is it possible to take this matrix model, and generate an invertible matrix that is an approximation of the original matrix?


texts: What is the frequency transfer function when $x(t) = e^{-3t}u(t)$ and $y(t) = 2u(t)[e^{-t}-e^{-4t}]$

texts:
What I did was take the fourier transform of both $x(t)$ and $y(t)$ and then divided $Y(j\omega)/X(j\omega)$. So
$$Y(j\omega) = \frac{2}{1+j\omega}-\frac{2}{4+j\omega}\quad\text{and}\quad X(j\omega) = \frac{1}{3+j\omega}$$

However, the answer is of the form: $\displaystyle \frac{A_1}{1+j\omega}+\frac{A_2}{4+j\omega}$ where the $A$'s are constant. I am not getting the solution of this form. I got $Y(j\omega)$ in this form, but not $H(j\omega)$.

Am I doing something wrong?


texts: I was reading through the Ambiguity function, and I was wondering if it's possible to calculate analytically (or numerically) the ambiguity function of a sum of sine waves. In case of a single sine wave the envelope is a rect(), hence the ambiguity function is a $sinc()$ with variables the delay time and the Doppler frequency. Here's  the respective 3D plot. Is it possible to perform a similar reasoning for multiple sines?


texts: Is there a process for deriving special cases of convolution?

texts:
For my signals and systems homework, I was met with the following problem:

Consider a CT system with impulse response given by

$$h(t) = e^{-|t|}$$

and a step input $x(t) = u(t)$. Using the deﬁnition of convolution, determine an expression for the output $y(t) = x(t)∗h(t)$.

I approached this problem using the standard method taught in my class. I set up the following integral:

$$\int_{-\infty}^{+\infty}h(\tau)x(t-\tau)d\tau$$

While evaluating the integral, I got stuck at the end as the integral approached infinity. I decided to rearrange $h(t)$ by expressing it in a different form. The form I then got it in was:

$$h(t) = e^{-t}u(t) + e^tu(-t)$$

Which then allowed me to match it to the following convolution on a table given with my homework.

From doing this problem it seems to me that there are special cases for convolutions. Ones that which the standard method of evaluation doesn't work.

Is there a process to derive these special cases? If so can an example be given? And why wouldn't the standard process work for this example?


texts:
I am trying to understand what happen when we take FFT2 of a matrix in a matlab.

first have a look at this simple example,

a=ones(8); %8x8 Matrix of Ones
fft2(a)

it will generate the following output,

    64     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0

in above matrix , 64 is the sum of all the matrix values and it is the DC coefficient.
Does that mean the 64 is calculated as 8*8 = 64 ?

Now the actual question,
i generated a matrix of 4,4,

   a = [zeros(4,2) ones(4,2)]

% 0     0     1     1
% 0     0     1     1
% 0     0     1     1
% 0     0     1     1

First 4 rows and Two columns are zeros while the remaining are ones as shows above.

Now if i take its FFT2,

    fft2(a)

It generates the following output,

  8.0000            -4.0000 + 4.0000i         0            -4.0000 - 4.0000i
        0                  0                  0                  0
        0                  0                  0                  0
        0                  0                  0                  0

According to the book, the values shown in the output are the DC coefficient and it is indeed the sum of all the matrix values.

In previous example it was easy to calculate the DC coefficient but in this example how these values are generated ?

  8.0000            -4.0000 + 4.0000i         0            -4.0000 - 4.0000i

If i calculate the fft instead of fft2 it will give the following output

%FFT -> DFT of Vector
%FFT2 -> DFT of Matrix
 0     0     4     4
 0     0     0     0
 0     0     0     0
 0     0     0     0


texts: I've found this diagram in a slide, but i have no backround to properly understand it. Could you explain to me, in simple terms, how this process behaves and what's the purpose of the blocks $z^{-1}$ ?


texts:
I am on my first DSP project where I want to implement lowpass/highpass filters for ECG application. I have started from MATLAB to give me orders and coefficients for my desired specs. I prefer to go with FIR filters but as you know they require much higher orders than IIR filters. Since this is my first project I have no clue what ballpark should I have in mind for a filter order that runs in a DSP.(Analog Devices BlackFin)

So I decided to frame this question as a general call for advice, that what filter orders are DSP engineers comfortable with choosing for implementation. Is 100's of order very high for a DSP? Do they go with less than order of 10? 50?

I understand this is very much dependent on filter specs and my application. But I still want to know if there is a range to have in mind.

I hope I have been able to convey my question.


texts: How does salt and pepper noise occurs in an image

texts: How does salt & pepper noise occur? And, what are some techniques to remove it?


texts: What does it mean for a dynamical system to be well-behaved?

texts:
I have recently stumbled across a paper about learning arbitrary dynamical systems in a spiking neural network. The paper assumes an underlying dynamical system of  the form $\dot{x}=f(x)+c(t)$ where $c$ is just a random input and $f$ can be a non-linear function.

The paper also states that the dynamical system must be well-behaved. I could not find anything understandable on the web. Can somebody explain this to me?


texts: Does only filter coefficients can represent it's own filter characteristic?

texts:
I'm wondering that does only filter coefficients can represent it's own filter characteristic?

I found filter design tool as FILTERDESIGNER of matlab. that can make filter coefficients of low pass filter or band pass filter or high pass filter etc as the below.

But I want to know what if there is only information of coefficients without information which is Response Type such as low or high and band filter.

Can we know that coefficients was made originally for low pass filter with  h[k]*x[n-k] equation?


texts: Pulse Doppler Radar: how to filter its Range-Doppler matrix?

texts:
I want to simulate a Pulse Doppler Radar with medium pulse repetition frequency (PRF about $100\textrm{ kHz}$, about $500$ pulses in pulse train).

It's rather powerful, and should discriminate targets with $1\textrm{ m}^2$ RCS in ranges up to $200\textrm{ km}$. Okay, let's build its range-speed image (about $\pm 750\textrm{ m/s}$ in speed dimension, about $1500\textrm{ m}$ in range).

But there is a problem: when there are some targets nearby (about $10\textrm{ km}$) they give not just a peak that can exceed the discrimination threshold, but a cross-like figure (sidelobes in range dimension, end, especially, sidelobes in speed dimension). And if the target is close enough, freaky sidelobes still can exceed the threshold and be treated as target candidates.

Even if I use window function with heaviest sidelobe-cancelling effect (Blackman-Harris), the sidelobes became smaller bus weren't wided out completely (and still give me ghost targets).

I think that I missed some important step in Range-Doppler matrix processing. Maybe some additional filtering. Cannot you tell me, what shoud I do to get rid of the sidelobes?

Here's some illustration: on the top row there are Range-Doppler matrices for different PRF ratios, and on the bottom row there is the range-speed matrix slice by speed (left) and range(right) in the target peak. The speed dimension annoyes me most = )

P.S. The number of DFT bins: 540 by speed, about 1200 by range (1200, 1280 and 1360, because PRFs varies).

About the size of the sidelobes -- I don't know how to add the colorbar to such a multi-plot figure, but I've added two additional plots to the bottom. In the left-bottom corner there is the signal power with different speeds (with the fixed range of the max peak range) and in the right-bottom corner there is the signal power with different ranges (with the fixed speed of the max peak speed). The units are power dB.


texts: Looking for a Mathematical Derivation for the Energy Formula in Continuous-time Domain

texts:
I have just started my signal and system course and I would like to know how we derive the corresponding formula for the energy of a continuous-time signal $x(t)$ over an interval $[t_{1},t_{2}]$ :

$$E_{x}=\displaystyle\int_{t_{1}}^{t_{2}}|x(t)|^{2}\;\text{d}t$$

That is to say why is the signal energy the area under the region of the square of $x(t)$. For instance, I can think of $x(t):=t$ with $t$ being geometrically the first bisector and so by squaring it we obtain a parabola so this would mean the energy is the area under this parabola but why is this true?


texts: Image Processing - What Is a Gradient Domain?

texts:
What is the gradient domain? Does it relate to the Laplace Pyramids?

I found only articles assuming you know what it is and not define it, can someone please define what is it and what it is used for?

The reference used is Seamless Image Stitching in the Gradient Domain


texts: How to remove weak edges in a binary photo?

texts:
See attached photos for reference.

I tried watershedding, it breaks apart the main body and doesnt even touch the part I want disconnected!

morphology is no good, the holes in the main body easily break in two before the edges I want disconnected come off.

imfill doesn't solve this, it fills the hole between the two trouble areas as well as the holes in the main body.

I have thousands of similar photos, so I need to come up with something robust.

I'd appreciate any help I could get!


texts: Sequence expansion by zeros and interpolation - does it insert additional frequencies?

texts:
I am struggling with understanding the consequences of oversampling on the frequency spectrum of the signal.

If I understand correctly, with an oversampling rate of 8X we insert 7 new values for each value measured. In case we keep this new values at 0 then we are not inserting any new frequencies to the signal, so the frequency spectrum should stay the same.

On the other hand, if we interpolate the new values eg by averaging the adjacent ones, then we MIGHT generate some new frequencies, that might appear in our frequency spectrum. This new inserted freuquencies will be of higher magnitude and should be filtered out if we want to keep the signal as "clean" as possible.

Am I correct with my understanding of oversampling and interpolation? Thanks in advance for any answer!


texts:
Introduction
I wish to design a pilot signal which will be used to estimate the channel, and will be sent prior to data, on a wireless acoustic link (underwater acoustic communication).
I've been reading on the matter, but I'd like some pointers. I should state that I don't care about things like bandwidth regulatory restrictions and such as no restrictions exist. I'm however limited by the bandwidth of my analog frontend, and possible sampling frequency.
I intend to use a matched filter at thr receiver which hopefully will be able to provide me the delays between echos.
My thoughts so far
I thought of using chirps due to their natural resilience to multipath. I currently have the following questions:

I consider using a single longer chirp, or a few shorter ones, possible "coding" them by using a short pn sequence. Is there an obvious preference to use either one?
I considered using some pulses shaping filter, so as to to incorporate it into my match. filter. My fear is that without it the analog frontend will distort the signal affecting the matched filter performance. Am I correct to consider this? How will the pulse shaping affect the autocorrelation properties of the chirps.
If i use a root raised cosine filter, are there any standard guidelines regarding choice of beta?

answers as well as relevant links will be appreciated


texts: If the mean of a random process is constant, does it imply the process is first order stationary?

texts: If a random process is first order stationary, its mean is constant. However, if a random process has a constant mean say $3$ and an autocorrelation equal to $9 + 15e^{|-\tau|}$. The process is clearly wide sense stationary. Is the process first order stationary?


texts: What is imaginary part after IFFT and how to use it?

texts:
let's say we have signal in time domain.
After we make FFT on it we will receive that signal in frequency domain.
And as far as I know the real numbers mean magnitudes of each frequency bin, and imaginary numbers mean phase shifh of each frequency bin.
And then if we make inverse FFT we get again the the signal in time domain.
And as far as I know that signal is expressed by real result of IFFT.
But then what mean imaginary part of IFFT output?
And - what is also important - how to use it?
I am asking because I have problems with phase synchronising after IFFT so I wonder that maybe that imaginary part of IFFT has something to do?
What is very strange for me is that I have exactly the same algorithm and I get totally different results on two various computers.
I created the clean sine wave oscillator. And I use it to test my FFT->IFFT algorithm.
And on one machine it seems like phase is synchronised properly if my FFT->IFFT size is 4 times buffer size. I mean that for each one buffer (let's say size 512) I calculate FFT->IFFT size 2048. Where first 512 samples are my sine wave, and the rest 1536 samples are just zeros. And I get quite good results.
But on other machine with exact the same algorithm, the same buffer size 512 and the same sample rate 44100 I have phase issue that cause my signal sound awful.
I have no idea why it is happen. The only thing which come to my head is that the machine with awful IFFT signal is just slower and the awful sound is not caused by unsynchronised phase but because of gaps between each buffer. But I can't believe it while both machines are similarly powerfull.
So finally the main question is how to ensure phase is always synchronised after IFFT. And how to do that to work on all machines the same?
For any help great thanks in advance.


texts: Do all Harmonics of a periodic sound start from a 0 base

texts: I've been thinking about additive synthesis and I'm wondering if all sounds begin at (theoretically) phase 0?


texts: “The Fourier transform cannot measure two phases at the same frequency.” Why not?

texts:
I have read that the Fourier transform cannot distinguish components with the same frequency but different phase. For example, in Mathoverflow, or xrayphysics, where I got the title of my question from: "The Fourier transform cannot measure two phases at the same frequency."

Why is this true mathematically?


texts:
I want to ask about this scheme:

$u_0$ should be something as input in specific point given by the initial conditions and $y_0$ output. Block State Spase represented linearized system by A, B, C, D state metrices.

And I'm wondering why there is "-" by $u_0$ and "+" by $y_0$. Is this scheme universal? Why does it look like it looks?


texts: How do I process IQ data received from a signal analyzer

texts: I used a signal analyzer to get IQ sample data from a blue tooth device. The IQ data received is in the form of a .MAT file and I examined the file contents and see an + ibn samples where a, b are constants, n is the sample number and the format is a complex number. I was told the real part is the I and the imaginary part is the Q. Are these samples received baseband I Q data? I am trying to determine the carrier frequency offset. I was trying to determine the frequency of the signal. I felt I could measure the phase difference between samples per time. However, I have the angles being only between pi/2 and -pi/2 when I do arctan(b/a). I assume I should unwrap the signal phase. In MATLAB there is the unwrap command (var = unwrap(phase)). But that does nothing to the values I received. I am unsure of how to proceed with my search for the carrier frequency offset. Any help?


texts: Reconstructing time domain signal with Hanning window

texts:
I am currently working on a frequency domain real-time application on a digital signal processor. Currently for one time frame of my algorithm I read in time domain data into a buffer, perform a Fourier transform with a Hanning window (win), which I generate using MATLAB with the following code:

win = 2*hanning(N,'periodic')/N;

where N is my transform length, (usually 2048 in my case). The window coefficients are then stored in a header file as single floating point data to be included into a C project.

In the frequency domain I execute my algorithm, then convert it back to the time domain to be outputted in a third buffer. I am certain the forward and reverse transforms work correctly having thoroughly tested them (and having used them for several months).

However when I output the data I use the following 'window' to reverse the effects (i.e. the energy level of the time domain signal to remove the 'oscillating' effect of the reconstructed signal) of the original window that I applied (in MATLAB code):

win_out = win ./ (win.^2);

I've seen the divide by energy (win.^2) in other peoples code, and assume that the line of MATLAB code above is equivalent to (it gives the same result of course):

win_out = 1./ win;

When I implement this in my real time application the values on the edge of my 'output' window (win_out) are very large (of the factor x10^8, see image below) and are in fact too big. This results in the edges of my time period being amplified too much resulting in a 'clippy' effect in my time domain signal when I listen to it.

I've illustrated the problem below

Above is the original reconstructed time domain signal, if this was to be outputted it would have an oscillating effect on the output, which I try and fix by applying an 'inverse' window.

This is the inverse window that generated by the above MATLAB code.

Time domain signal with my 'inverse' window (note: spikes at each end).

First spike zoomed in.

NB: I don't use overlapping (yet!)

My question is: how do a choose an 'inverse' (if that is the correct term?) window to ensure those spikes aren't present in fully reconstructed time domain signal with window?

Many thanks !


texts: How to conclude LTI, causality and BIBO stability of a system represented by a differential equation?

texts:
I have started to learn about systems represented by differential equations in Oppenheim's Signals & Systems, and I got really confused about it. I am trying to understand how I can show that a system is LTI (or not), causal (or not) and BIBO stable (or not) for any input.

I know the following (please correct me if I'm wrong):

If the differential equation has zero auxiliary conditions then the system is linear. Therefore, showing linearity is easy.
A system is defined by the response to the Dirac input.
Causal, LTI $\iff$ initial rest (mathematically meaning if $x(t)=0$ for $t<0$ then $y(t)=0$ for $t<0$).

I am not sure if I got it right but if I'm willing to use #3 in order to show that the system is causal and LTI, then it has to have initial rest for any input. How can something like that be shown if as I say it has to be for any $x(t)$? I thought that maybe using #2 will be helpful (solving for the differential equation for delta function and then somehow to show), can it be?

In conclusion, I would thankful if you explain to me how show those features when I got a system that represented by differential equation. For example, in case that we got that simple ODE:

$$\frac{d^2y}{dt^2}-3\frac{dy}{dt}+2y(t)=x(t) \ \ \ ,y(0)=\frac{dy}{dy}=0$$


texts: What are the audio equivalents of images like "Lena", "Mandrill", and "Cameraman"?

texts: I don't know what to call these images, but they're very often used in the image processing world as standard examples to show the output of a particular operation. Here's a link to the page describing Lena as a "standard test image". Are there similar canonical audio clips used to demonstrate the effects of certain audio filters or operations?


texts: How to select the order of LPC to model formants?

texts:
I am having some difficulties understanding LPC and speech processing in general. The professor asked us to provide an heuristic way to select the order of LPC? For example if I wanted to model 3 formants what would be the order I should use? I understand the order of prediction is the number of coefficient used in the estimation of the signal $s(n)$:
$$\hat{s}(n)=\sum_{k=0}^p a_ks(n-k)$$
I am also open to any resources for a beginner in automatic speech recognition.


texts: Cross-correlation or cross-covariance of non-zero mean signals

texts:
Cross-correlation for uniformly sampled signals is defined as [1]

$$(f \star g)[n]\ \stackrel{\mathrm{def}}{=} \sum_{m=-\infty}^{\infty} f^*[m]\ g[m+n].$$

Cross-covariance for wide-sense stationary (WSS) signals is defined identically [2]. This seems strange to me, because the statistical definition [3] first subtracts the signal means from the signals before correlating it with each other. In other words, cross-covariance is substantially different from cross-correlation if the mean of the signals is substantially different from zero (is the Wikipedia article wrong? Or does it somehow assume zero mean signals?).

So, cross-covariance equals cross-correlation if the signal means are zero, else it is unequal.

Questions:

What are reasons to choose for cross-correlation or cross-covariance when comparing signals with non-zero mean?
Does cross-correlation have any significance in this case, because $f\star g$ has mean $\mu_f\mu_g$?
How would one find out the cross-correlation of signals that are not WSS, e.g. the mean is a linear trend? What would happen if we'd ignore this linear trend and simply subtract the signal means, then calculate cross-correlation? What if we subtracted the linear trend instead of the mean? What are the consequences for such mild violations of WSS-ity?


texts: How can I convert a step response that is described by the sum of two exponents to an IIR filter analytically?

texts:
If a system has the following step response:

$$\begin{align}
y(t) &= 1 - \Big(A e^{−t/T_1} + (1-A) e^{−t/T_2}\Big) \\
 &= 1 - A e^{−t/T_1} - (1-A) e^{−t/T_2} \\
\end{align}$$

and I know the values of $A$, $T_1$ and $T_2$, can I transform this to a discrete-time IIR filter analytically?  If there is no analytical solution, is it possible to say how many poles/zeros the IIR filter should have?

I've done it numerically by using the Prony's method on the impulse response, but I'm hoping there is a more direct way.


texts:
What are the formulas for signal and noise power gain of digital filters (FIR and IIR)?

For a FIR, I've seen in Harris' windowing paper that the DC gain is the sum of the filter weights.

$$
G = \sum_{i=0}^{N-1} w_i
$$

For a FIR, I've seen that the noise gain is the square root of the sum of the square of the weights.
$$
G = (\sum_{k=0}^{N-1} w_i^2 )^\frac{1}{2}
$$

What about an IIR?


texts: Conceptually confused by LPC for speech: Do we synthesize by the inverse filter (FIR)?

texts:
I've been following the process of using LPC to analyse the speech and then synthesize the speech by swapping out coefficients over time. I'm purely concerned with pitched vowels at this point.

lpc(speech_segment) gives us $a_{p}$ coefficients of an IIR filter, where $p$ is the order. This IIR filter has the frequency response of the speech vowel/formant present in speech_segment.

I have a pulse train to use as a source.

I see two ideologies for synthesis:

some texts talk about using the IIR filter to filter the source, which makes sense to me intuitively - juxtaposing the vowel's frequency response to my source's spectrum
Other texts talk about using the inverse of this IIR filter to form an FIR, and then filter the source somehow. I think I understand why this is invertible and stable (minimum-phase).

So approach 2 makes less sense to me from source-filter perspective, but it would be really useful because it means I can perform LPC analysis-synthesis with OLA convolution of audio blocks rather than implement the filter recursively.

Is my understanding of either of these two approaches, not quite right? If not, what exactly changes to make each possible.


texts: How to convert wave from real to complex and vice versa?

texts:
I have wave expressed by array of real numbers (double in C++). But I want to express it as a complex.
I tried to create complex variable and assign to its real the array of my wave and to its imaginary just array of zeros. OK it's complex now. But I feel there is something wrong. It's not authentic complex. It's just surrogate. For example I can't manipulate in phase (only reverse phase). When I multiply it by for example $ i^{0.4} $ it's just changing amplitude little bit but phase is without change.

In the other hand if I have authentic complex wave how to express it as a real numbers but including information from imaginary values?

For any help great thanks in advance.


texts:
I'm trying to detect a sync word in a signal using Symmetrical Differential PSK (bit 0 = +90° phase, bit 1 = -90° phase).

Given the signal is encoded in the phase difference between two symbols, the absolute phase is irrelevant. How would I go about using cross-correlation to detect the sync word?

I have four possible orientations for the sequence considering the absolute phase, but for performance reasons, I would prefer not to run the cross-correlation more than once. Should I calculate the phase difference of each symbol with the previous (i.e. extract the bits) and correlate on that or is there a way to do it without first converting the signal to bits?


texts: Say we have a 12-bit ADC with 30 MHz sampling frequency. I want to perform several DSP operations on output digital signal so that resulting signal would have increased accuracy to 14 bits and output sampling frequency would become 2 MHz. In nutshell I want a DSP block that converts a 12-bit ADC with 30 MHz Sampling rate to a 14-bit ADC with 2 MHz sampling. Even a slight tip for me to know where to look for would be helpful. (This project would be implemented on a FPGA.)


texts: How to use Robust PCA for image inpainting?

texts:
I want to use Robust PCA for image inpainting, i.e. to estimate anomalous (bad) pixels. I assume that the bad pixels are known (mask).

I know how to calculate the Robust PCA using Alternating Direction Method of Multipliers but if somebody has already an implementation in Matlab I would not say no to sharing it. ;) But this is not my question.

How can I use Robust PCA for image inpainting, i.e. estimating the bad pixels? With Robust PCA I have X = L + S where X is my original image matrix for some training images, L is a low rank matrix and S is a sparse matrix.


texts: Phase shift of all-pass bi-quadratic filter

texts:
Does anybody know how to derive this phase function for that all-pass filter structure? Many papers re-print them, and corresponding chart as well.

But nobody mentions that at normalized frequency 0.25, tan(pi/2) goes to +- infinity, and atan jumps from + to - pi/2 :

Is phase shift periodic here by pi, so we can move the right curve down to glue them at 0.25. What does that mean in real filter operation?


texts: SNR estimation: signal with unknown amplitude and Gaussian noise

texts:
I would like to know can anyone suggest me techniques to estimate the SNR for a given noisy signal. I do not know the amplitude of my signal but I do know that noise is Gaussian.

I have tried to do estimation in frequency domain where I simply take the FFT of the signal and find the dominant peak and find the power associated with that as the signal power and noise power as the power in all other bins.

However, this technique seems to work well when I have sinusoidal signal and fails easily when I just have a noisy signal and do not know the nature of the signal since I do not know what peaks in FFT corresponds to my signal and how many of them.


texts: Vector based video coding, could it match the latest hybrid coders?

texts:
I could not find any image/video/media coding stackexchange so I thought that maybe this one would be the best fit.

It seems to me that the state of the art in video coding is constantly being pushed forward in terms of bigger macroblocks, more sophisticated hybrid coding control circuitry, more and more post- & pre- processing filters ( example deblocking filters ) and more modes of operation for basically everything in the machinery of ever growing complexity.

Does there exist any vector based coding technique which is anywhere near being able to compete with the latest hybrid coding technique standards like h265, VP9 et.c.

What do you think are the main reasons for why vector based video codecs aren't being investigated to a larger extent?

Personally I think it is because of too much work involved in developing a whole new framework where it is easier to just go on with more advanced variations of an already proven concept.


texts: I am not specialist in DSP,I am dealing with geophysical time-series(electromagenteic sources).After converting to frequency domain,my friend is trying to filter with FIR(45-65Hz) to get rid of AC noise(50Hz).The questionis about the harmonics,how will FIR filtering influence harmonics?


texts: Efficient way to get power levels from an SDR (RTL-SDR specifically)

texts: At the moment I can step through the frequency band of interest and take samples to estimate relative power at various frequencies.  But this is slow.  Is it effective to center myself in the band of interest, make sure my sample rate is high, and do an FFT instead?  I'm just wanting to efficiently get relative power levels for frequencies throughout a band.


texts: Effect in Fourier-domain when the signal is "zero-stuffed" in time-domain

texts:
Suppose $x[n]=[x_0,x_1, \ldots,x_{N-1}]$ and $y[n]=[x_0,0,x_1,0,\ldots,0,x_{N-1}]$. What is the relationship between the Fourier Transforms of both the signals?

When I try for some specific examples in MATLAB, I see that $Y[k]$ has an image of $X[k]$ but how do we show this mathematically?


texts:
I've read about the PSD of one OFDM symbol for instance being an estimate of the PSD, but how can it be an 'estimate', when it literally is the PSD of that OFDM symbol.
What is actually being estimated? I get that the OFDM symbol is supposed to be a single record of a WSS random process, and therefore its an estimate of the PSD of the random process because you can't calculate the expected value. But why would you want to calculate the PSD of 'the random process' and not just a single OFDM symbol – surely that's the granularity of focus.


texts: STFT - Plotting is not a true representation

texts:
I might be going crazy here. Following my question: here

I did some thinking and probably understood that my STFT algorithm was not performing correctly.

I followed this algorithm:

-> Get 256 of data

-> Apply windowing function

-> Get the FFT

-> get the first 128 points

Here is my result. I have used NFFT = 256 which should give me 128 points. I firstly calculated the FFT (after the windowing function was applied) and only counted the first 128 values of this. I.e. FFT_RESULT / 2

Whereas my last output was the following:

I don't quite understand why the values along the X axis are particular that high?

EDIT:

Ok, so following the advice, I did the following:

1) Created a 2D vector for each of the "256 resulting FFT values"

for(size_t i=0; (i < signal.size()); i++)
{
    std::vector<double> temp_vector;
    // store blocks of 256 inside temp_vector

    // Compute Hanning Window

    // Compute FFT

    std::vector<std::vector<complex> stft;

    stft.push_back(temp_vector);
}

This gave me a total of 74 blocks within the 2D vector.

I then took the absolute value of the REAL values and stored these inside a double, read these in and with pylab library I used imshow() and got the following result:

However, If I plot normally, I get the following:

I think my calculations are correct, I just don't think I'm plotting them right using the spectrogram!!


texts: Difference Equation - Time Response analysis of Discrete Systems

texts:
We know that that the difference equation formula for computing an output sample at time $ n$ is based upon its past/present input samples and past output samples in time domain:

$$
\begin{aligned}
y(n) &= b_0 \,x(n) + b_1 \,x(n - 1) + \cdots + b_M \,x(n - M) \\
&\qquad- a_1 \,y(n - 1) - \cdots - a_N \,y(n - N) \\
&=\sum_{i=0}^M b_i \,x(n-i) - \sum_{j=1}^N a_j \,y(n-j)
\end{aligned}
$$

My question is why $j$ begins from 1 rather than from value 0 like for $i$ and also how can we write the below output equation in difference equation form:

$$
\begin{aligned}
y(n) &= 0.01\ x(n - 5) + 0.002\ x(n - 1) + 0.99\ y(n - 1)\\
y(n) &= 0.01\ x(n) + 0.002\ x(n - 1) \\
y(5) &= 0.01\ x(3) + x(1) \\
\end{aligned}
$$

Secondly why $y(n)$ sequence values are calculated as a sum of a series of input / output, cause I have been studying that $$y(n) = \{2,4,6,8\}$$ when $$x(n) = \{1,2,3,4\}$$ and $$n =\{1,2,3,4\}$$ (example per say) i.e. $y(n) = 2\cdot x(n)$.

There was no mention that for $y(n)$ ($y(2)$ say) value we need to add values of $x(n)$ and $y(n)$ i.e. (take values of $x(1)$ or $y(1)$) or $y(n-1)$)?


texts: How to normalize the power of a QAM signal?

texts:
If I have, for example a 16-QAM signal, and the constellation points are (3,3),(3,1),(1,3),(1,1),...(-3,-3).

Now I have a simulated in coming signal with arbitrary power, how can I normalize the signal to this constellation so I can make correct decisions?

The first thing I could think of is to calculate the average power of the in coming signal and normalize it to the average energy of the constellation. But then when I have a very noisy signal, the noise power will effect the scaling factor considerably.

So is there some kind of least mean square method that I can implement so I can really get the scaling correct?

BTW I'm using Python/NumPy/SciPy for my simulation.


texts: How to find peak frequency in an audio frequency spectrum?

texts:
I have a audio file consisting of multiple frequencies, I need to find all the frequency peaks in the frequency spectrum after doing FFT.
But the issue is how can I be able to set the threshold line for the peaks.

As you can clearly see I need to find all the peaks of this spectrum but sometimes amplitude is very high and sometimes it is too low so how will we be able to know the exact frequencies present inside audio.
If we set amplitude threshold to 0.5 the peak present at 17000 Hz  will now count but if we set it too low then sometimes noises becomes larger than the value itself.


texts: Background Removal and Object Tracking - Track Fish Jumping Out of the Water

texts:
0 down vote favorite

I am totally new to Image processing. I just started my Master thesis in the area of Computer vision and Machine learning. My background is Informatics. Now, my first task is to register the images of some fishes(Image registration) as they come out of water. I have got stream of images and I want to come up with a model of the fish by aligning the temporally different images of a fish. As, I can understand, I will have to fist of all remove the background and water from the images to work on just fishes, am I right?

Can anyone give me a brief idea of how I should go forward or the things I should read first before I can understand the things. For example, should I read the basics of Image Processing, Feature detection, Image segmentation....? and regarding the programming language I can use - one where I can find good libraries, forums, other help.

I would be really grateful, if anyone can help. Thanks


texts:
I started studying DSP recently. In my MATLAB assignments, I am often asked to plot the frequency response of a digital filter using freqz. I know there's another function for plotting a frequency response, bode.

In my last assignment, I was asked to design a notch filter for $60\textrm{ Hz}$ with a sampling frequency of $200\textrm{ Hz}$. After doing so, I plotted the frequency response using freqz, which gave me the expected result - the notch was on $60\textrm{ Hz}$:

However, when I plot the frequency response using bode, the frequency is off significantly:

To my understanding, both functions measure the frequency response. Why is one giving me the correct result then, when the other is not?


texts:
I do like to generate the FFT from time domain history data (experimental lab) using MATLAB. I am not so sure if my coding is right? Can someone verify the coding.

My code is as follow:

 clc;
 signalx = Ch1;
 N=6678;
 t=Time;

 %Plot FFT Vehicle signal
 zx = fft(signalx);
 plot(abs(zx));
 title('FFT Vehicle');
 xlabel('Frequency [Hertz]')
 ylabel('Magnitude');


texts:
i've written a source code in visual dp ++ in c language. the platform is sharc processor adsp 21062.after the build is complete. while running the program it is displaying a message
 Instruction timed out with PC at: 0x20a5a . what may be the error in my c code. can you please resolve?


texts: Recommendations for learning and getting hands-on Real Time Signal processing

texts:
I know this is not a technical question, but wanted to get some opinion on how to get some hands-on experience on embedded DSP / real-time signal processing
I am comfortable with DSP and wireless communications simulations in MATLAB /python and wanted to get into embedded DSP development and I'm not able to get any structured way of learning real-time DSP (I regret not taking RTSP class in my masters) . I'm proficient in C and have a very basic level knowledge in  assembly. I'm ok to buy the hardware for my learning curve.
I tried searching for any online training /course from universities which offers such class where we start writing some vector DSP code on the embedded platform (TI or ARM etc).
Any recommendations/insight into this would be highly grateful.
Thanks
Saira


texts: Is there a way to detect ambiguous edges?

texts:
I'm writing a program that can detect veins(the dark lines) on an arm.

When looking at the image at full size, you can easily make out where they are.

But when zoomed in around a vein I get something ambiguous which doesn't seem to have edges anymore.

I've tried edge detection but it doesn't work well since the apparent 'edges' aren't actually edges when viewed close up.

Took me a while to learn all the necessary mathematics, but I've managed to write a ridge detection algorithm as suggested by Rethunk. This question helped alot.

It works quite well.

Still needs improvement though, probably using scale space image processing as suggested by Fat32.


texts:
Hi I am trying to use a low pass filter in Matlab. I am trying to use the simple butterworth filter.

I have defined dataset say "data". Then I created the butterworth filter as follows:

[B,A]=butter(2,0.01)

Butterworth design require the user to give N and Wn. I used N as 2 and Wn as 0.01. Here, I randomly chose the value of Wn to 0.01.

My data is a hourly data and I want to apply 48 hour low pass filter. What would be the cut off frequency in my case ?

After that I used the following code to design a filter:

filter(B,A,data)

The filtered data looks good but I want to know what cutoff frequency should I use.

Thanks.


texts:
I have very limited knowledge of DSP, so I apologize if my question is trivial :)

I have an EEG signal from which I need to extract different frequency bands. For example, waves in the the frequency band of 8-12 Hz.

After noise filtering, I was planning to simply feed the data into the FFmpeg bandpass filter, setting the 'frequency' to 10 Hz, and 'width' to 2 Hz. Is this the way to do it?

I need to ask this since I'm not sure how to check if I got the correct wave in the end.


texts: Using GavabDB for 3D face reconstruction from frontal image

texts:
Project: 3D face reconstruction

Input: 2D frontal face Image Output: 3D face Reconstruction and expression simulation Platform: Matlab or Opencv cpp.

I found out after study that 3D Morphable Models (3DMM) algorithm is a good starting point for my project. But I don't have the Basel Face Model (3D face Database) to implement the algorithm. However, I have downloaded GavabDB from http://gavab.escet.urjc.es/recursos_en.html. Can I develop 3DMM using the GavabDB for 3D face reconstruction from frontal image? After reading the dataset description doc, I observed that Gavab doesn't provide Texture data of the 3D scans; is texture data compulsory?

Does the output quality depend on the 3D database used for modeling?


texts: For single tone transmission impaired by IES, how Doppler Spread is translated in Channel impulse response computation?

texts:
If we are to transmit in single tone transmission in a Single Input Single Output configuration. And the channel is impaired by awgn and inter symbol interference with the following characteristics:

2 paths with Gaussian Doppler spread shape,
delay of 0 ms, amplitude gain[dB] 0.5, doppler shift 0Hz, doppler Spread (standard deviation) 0.1Hz,
delay of 2 ms, amplitude gain[dB] 1,   doppler shift 2.4, doppler Spread (standard deviation) 2.4 Hz,
Sampling rate $4800Hz$, bandwidth of transmission $6kHz$.

Here  are my thoughts to compute channel impulse response CIR:

First compute the length of the CIR: take the longuest delay (delay spread) divide it by the sampling period. In this example : $\frac{2 \cdot 10^{-3}}{\frac{1}{4800}} = 4800 \times 2 \cdot 10^{-3} = 9.6 \approx 10 $ ==> the CIR spread to $10$ symbols.
init the CIR vector named $h$ to all zeros except at the delay indices, i.e,
$h(i) = 0 \quad if \quad i \quad \neq 0 \quad or \quad i \quad \neq \frac{2 \cdot 10^{-3}}{\frac{1}{4800}} = 4800 \times 2 \cdot 10^{-3} \approx  10 $. For those two indices, apply the two gain $[0.5, 1]$.
Compute the Doppler for each individual tap and apply it. For that we first determine an optimal intermidiate sample rate $f_m = 32 \times f_d$; we generate white gaussian noise with this rate and filter it in order to obtain the desired spectrum. And then interpolate the output signal to the symbol frequency ?

My question is how to make the last step ?


texts: Choice of cost function in adaptive noise cancellation

texts:
Why is the least squares cost function used in adaptive noise cancellation with the recursive least squares (RLS) algorithm, but the mean squared error used in signal estimation?

For an ergodic source (where time and ensemble averages should be the same) I would have thought the choice was arbitrary.

From my notes: LMS minimises $\|e[n]\|^{2}$ and RLS minimises $\sum_{i=0}^{N} e^{2}[i], $
where $e[n]$ is the difference between the desired signal and the output of the filter.


texts: In a book by Alan Oppenheim, it is given that for a LTI system, its characteristics are completely determined by its impulse response. But if impulse response of a system is basically an input output relation and impulse response can be different for the same system depending upon our choice of output, so how does it completely characterize the system? Isn't it  contradictory? And is complete characterization of system also include stability of system?


texts:
https://clips.twitch.tv/TangentialObliqueLobsterSaltBae
https://clips.twitch.tv/CharmingBashfulAlfalfaRickroll
https://clips.twitch.tv/NaiveKindGorillaGivePLZ

(Disclaimer: These were not recorded on or uploaded from my computer.)

In the 1st video linked above, the water sloshing sounds heavily distorted and the same type of "noise" heard throughout that segment of the clip can be heard periodically throughout this person's videos, including the other ones I linked.

I've been trying to help this person hear the problem with his audio, but he's not hearing it and I'm not entirely sure what the cause of it could be or how one could even describe it.

EDIT: He switched to different broadcasting software and finally hears how bad it sounds now. Now we just need to know the cause.


texts: sampling a continuous time signal using MATLAB?

texts:
I have a continuous time signal $x(t)=cos(2 πft)$ where $0\leq t \leq 2$.

I want to plot discrete time signal $x(n)$ where $0 \leq n \leq 19$ for sampling frequency 100 Hz and signal frequency 10 Hz.

My MATLAB code is follow:

clc
clear all
close all
t=0:0.1:2
f=10
x=cos(2*pi*f*t)
subplot(211)
plot(t,x)
n=0:19
fs=100
Ts=0.01
x_a=cos(2*pi*f*n*0.01)
subplot(212)
stem(n,x_a)``

Please let me know, am I correct?


texts: Removing periodic spike noise from ECG signal

texts:
The signal shown in the following figure is collected from a ECG sensor. The spike noise that is observed with a periodicity of 30 seconds was traced to the periodic blip of the LED as it draws current.

The following is one instance of the spike noise after zooming in,

Frequency domain filters are not effective in this case because the frequency domain characteristics of the LED blip artifact is similar to the heart beat signal(QRS).

Is there any effective way to remove this artifact..? I was think of using the blip as a mother wavelet and performing a multi-scale correlation with the ECG signal to detect the spikes. Is this the procedure for wavelet denoising? Is there any other effective way of denoising for this case?


texts: Which sections to cover for my graduation thesis on blind source separation?

texts:
I'm not sure if I'm on right place to ask a simple suggestion, so please be kind and don't downvote my question. I'm not asking someone to do it for me, I just need short guidance how should I proceed.

Currently, I'm writing a study of Blind source separation using eigenvalue decomposition. Since I'm not good at writing, I have done so far the needed programming part in Matlab. The study must be composed of ~50 pages theory about the problem. Theory should be in terms of explaining the BSS, BSS methods, ICA, and EVD which is the main topic. Can you suggest what to include in my writing since BSS has a lot of methods and it is difficult for me to decide and follow what to write and what not write. Can someone outline the order of things I should write and mention in my study?

I'm stuck at what should I write next, so far I have:

Introduction to BSS
Definition of Independence of signals
Independence and correlation
PCA and other prewhitening methods:
        1. centering
        2. whitening

I'm using books like: Independent Component Analysis - A Tutorial Introduction Handbook of Blind Source Separation Independent Component Analysis and Applications 2010 - Pierre Comon, Christian Jutten

Thank you,


texts:
i have 2 audio signals, both available in time and frequency domain:
A: Noise
B: Noise(A with minor variations) + Additive sounds (C)

i want to eliminate Signal A from B to leave only C.
C is for testing almost zero, so after removing A from B silence would be the best.

My signals to visualize the problem:
Signal A:

Signal B:

Now my questions:
What would be the best approach to eliminate A from B?

I have tried to implement power spectral subtraction with no results as the signals seem to bee not similar enough to just subtract them. (or i did it wrong, i this case just tell me if this is the best way to do it)

As a spectrum of C would be sufficient a more graphical approach may be better? To smooth my fft data, compute power spectra (basically what audacity does in the pictures) and subtract them to see whats left? (should be C)?

Additional question:
how can i change the overall amplitude of a signal in frequency domain without "colouring" the sound? i tried multiplying all real and imaginary parts by x but this changes the sound.

any help appreciated!
regards


texts: Discrete representation of a signal that has unevenly spaced samples in frequency

texts:
I'd like to describe a problem that I've been struggling with for a while. I want to apologize in advance due to the long text. I just want to be as clear as possible in my first post.
Consider the equation below that provides a relationship between a variable $u(t)$, function of time $t$ ($u$ is given in meters) and the variable $B(z)$, function of a position $z$ in the space ($B$ is given in Tesla).
$$u(t) = \alpha \int_{-\infty}^{\infty} \frac{e^{i\kappa c \beta}-1}{\kappa^2c^2} \overline{B}(\kappa)e^{-i\kappa ct} d\kappa \, \, \, \, \, (1)$$
In this equation, $\kappa$ is the wavenumber (rad/m), $c$ is the wave speed (m/s), $\overline{B}(\kappa)$ is the Fourier Transform of $B(z)$, and $\alpha$ and $\beta$ are constants. It is clear to me that this equation is a representation of an inverse Fourier transform. (Maybe that becomes more clear if we define the angular frequency $\omega = \kappa c$).
Now, consider two things:

I need to represent this equation in the discrete world. In other words, I only have discrete samples of $B$ (i.e., $B(n\Delta z) = B[n]$ and, consequently, samples for $t$, $\kappa$ and $u$. If $c$ is constant (let's say $c_0$), I would try something like

$$u[m] = \alpha \frac{2}{N} \operatorname{Re}\left\{\sum_{n=2}^{N/2} \frac{e^{i\kappa [n]c_0}-1}{(\kappa [n]c_0)^2} \overline{B}[n] e^{-i\kappa [n]c_0t[m]}\right\} \, \, \, \, \, (2)$$
where $N$ is the number of samples, $\kappa[n] = 2\pi(n-1)/(\Delta z N)$ (evenly spaced samples) and $t[m] = m\Delta t$. This representation seems to work pretty well. Notice that $n$ starts from 2 because I am not interested in the DC component. Besides, for $n=1$, I'd have a division by 0.

Consider now that $c$ is not a constant, but instead, a function of $\kappa$, given by

$$c(\kappa) = c_0 \sqrt{1+a\kappa^2} \, \, \, \, \, (3)$$
or
$$c[n] = c_0 \sqrt{1+a(\kappa[n])^2} \, \, \, \, \, (4)$$
for the discrete samples, where $c_0$ and $a$ are constants. Can I still use the same representation of equation (2)? I've tried so, but I am afraid it would not be correct. The reason is because the exponential argument $k[n]c[n]$ (which corresponds to an angular frequency $\omega[n]$) is no longer evenly spaced. I do not know if I have to use something related to an inverse non-uniform discrete Fourier transform. In other words, if you have samples of $B[n]$ instead of the continuous function $B(z)$ and $c$ is given by equation (3), how would you represent equation (1) in the discrete domain?
Thank you. Take care. =)


texts: Video processing to detect a logo in frames

texts:
I am trying to detect a TV channel logo inside a video file, so simply given an input .mp4 video, detect if it has that logo present in all (or most) of frames or not (or maybe what percentage of frames include that logo). My aim is to classify ad and video portions (I noticed ads do not have the logo).

We have that logo in advance and the location is always fixed, so I believe the problem can be trivial to just a matching problem.

What is the best way to achieve this? Is there any tools or libraries that I can use for this?


texts: Does each pixel of the original image has a corresponding coefficient for every scale and every direction calculated by the DWT?

texts:
I want to take a pixel and find its coefficients calculated by the discrete wavelet transform for every scale and every direction. But as the DWT subsamples images, I don't see how to do that. Do I have to interpolate the coefficient matrices produced by the DWT?
In the non-subsampled contourlet transform for example this is not an issue because there is no subsampling. For each pixel of the original image I take the coefficients that have the same position in the generated images, but that's not possible with the wavelet transform because images get smaller and smaller in size.


texts: The number of bits per symbol is less than one

texts:
For a channel of bandwidth B Hz and signal-to-noise ratio of S/N, i have used Shannon-formula to calculate the maximum channel capacity C. For transmitting at the nyquist baud rate (2 symbol/sec), when i substituded in nyquist formula to find the number of levels, and used the number of levels to find the number of bits per symbol, i found that the number of bits/symbol equals 0.5.
What does this mean?  How can this be achieved?


texts:
I see often people here posting about GNU Radio, I hope mine is not in the wrong place.
I try to implement a demodulation chain and would like to measure its performance.
I added a BER block and it seems that I am not able to "reset" its accumulation. So the BER measure is biased by the transient while the demodulator is locking.
I would like to enable BER measure after a transient is done (after a given number of samples for example)
Is there a kind of known method to do this?


texts: Can someone help explain what this FFT workflow is doing to my signal, and why it works?

texts:
I am working with a piece of equipment that does acoustic analysis. It does this by acquiring a time domain signal and performing an FFT on it to extract the amplitude and phase at a single desired frequency, call it f0. Now, I understand the FFT. That part is easy enough. However, what I don't understand is the consequences of all the extra steps I found in this instrument's LabView code. Here's the procedure:

Acquire time domain signal and apply calibration coefficient to every point.
Subtract mean from signal to remove DC component
Mix with a pure tone at f0 by multiplying the complex time domain signal with cos(2πf0) - i sin(2πf0)
Window using exact Blackman
Perform FFT
Take DC component of output, divide by N/2 (where N is the number of samples in the time domain)
Get amplitude and phase at f0 from DC component

Specifically, I'm confused on how step 3 allows me to get the value at f0 by looking at the DC component of the FFT output. I've recreated this in python using numpy.fft.fft and some simulated signals and I get similar results.

At the end of the day, I guess this sounds like a theory/math question.


texts: In opecv function Hough circles how does parameter 1 and 2 affect circle detection and how can I adjust them to increase accuracy?

texts:
I'm using opencv houghcircle function to detect circles.

http://docs.opencv.org/doc/tutorials/imgproc/imgtrans/hough_circle/hough_circle.html

Problem is if I set minimum radius to null it detects wrong center and draws smaller radius circle or sometimes larger radius circle.  I'm looking for increasing accuracy of detection by adjusting threshold parameter 1 and 2.