librosa/feature/spectral.py
def spectral_bandwidth(y=None, sr=22050, S=None, n_fft=2048, hop_length=512,
                       win_length=None, window='hann', center=True, pad_mode='reflect',
                       freq=None, centroid=None, norm=True, p=2):
    '''Compute p'th-order spectral bandwidth:

        (sum_k S[k] * (freq[k] - centroid)**p)**(1/p)

    Parameters
    ----------
    y : np.ndarray [shape=(n,)] or None
        audio time series

    sr : number > 0 [scalar]
        audio sampling rate of `y`

    S : np.ndarray [shape=(d, t)] or None
        (optional) spectrogram magnitude

    n_fft : int > 0 [scalar]
        FFT window size

    hop_length : int > 0 [scalar]
        hop length for STFT. See `librosa.core.stft` for details.

    win_length : int <= n_fft [scalar]
        Each frame of audio is windowed by `window()`.
        The window will be of length `win_length` and then padded
        with zeros to match `n_fft`.

        If unspecified, defaults to ``win_length = n_fft``.

    window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
        - a window specification (string, tuple, or number);
          see `scipy.signal.get_window`
        - a window function, such as `scipy.signal.hanning`
        - a vector or array of length `n_fft`

        .. see also:: `filters.get_window`

    center : boolean
        - If `True`, the signal `y` is padded so that frame
          `t` is centered at `y[t * hop_length]`.
        - If `False`, then frame `t` begins at `y[t * hop_length]`

    pad_mode : string
        If `center=True`, the padding mode to use at the edges of the signal.
        By default, STFT uses reflection padding.

    freq : None or np.ndarray [shape=(d,) or shape=(d, t)]
        Center frequencies for spectrogram bins.
        If `None`, then FFT bin center frequencies are used.
        Otherwise, it can be a single array of `d` center frequencies,
        or a matrix of center frequencies as constructed by
        `librosa.core.ifgram`

    centroid : None or np.ndarray [shape=(1, t)]
        pre-computed centroid frequencies

    norm : bool
        Normalize per-frame spectral energy (sum to one)

    p : float > 0
        Power to raise deviation from spectral centroid.


    Returns
    -------
    bandwidth : np.ndarray [shape=(1, t)]
        frequency bandwidth for each frame


    Examples
    --------
    From time-series input

    >>> y, sr = librosa.load(librosa.util.example_audio_file())
    >>> spec_bw = librosa.feature.spectral_bandwidth(y=y, sr=sr)
    >>> spec_bw
    array([[ 3379.878,  1429.486, ...,  3235.214,  3080.148]])

    From spectrogram input

    >>> S, phase = librosa.magphase(librosa.stft(y=y))
    >>> librosa.feature.spectral_bandwidth(S=S)
    array([[ 3379.878,  1429.486, ...,  3235.214,  3080.148]])

    Using variable bin center frequencies

    >>> if_gram, D = librosa.ifgram(y)
    >>> librosa.feature.spectral_bandwidth(S=np.abs(D), freq=if_gram)
    array([[ 3380.011,  1429.11 , ...,  3235.22 ,  3080.148]])

    Plot the result

    >>> import matplotlib.pyplot as plt
    >>> plt.figure()
    >>> plt.subplot(2, 1, 1)
    >>> plt.semilogy(spec_bw.T, label='Spectral bandwidth')
    >>> plt.ylabel('Hz')
    >>> plt.xticks([])
    >>> plt.xlim([0, spec_bw.shape[-1]])
    >>> plt.legend()
    >>> plt.subplot(2, 1, 2)
    >>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
    ...                          y_axis='log', x_axis='time')
    >>> plt.title('log Power spectrogram')
    >>> plt.tight_layout()

    '''

    S, n_fft = _spectrogram(y=y, S=S, n_fft=n_fft, hop_length=hop_length,
                            win_length=win_length, window=window, center=center,
                            pad_mode=pad_mode)

    if not np.isrealobj(S):
        raise ParameterError('Spectral bandwidth is only defined '
                             'with real-valued input')
    elif np.any(S < 0):
        raise ParameterError('Spectral bandwidth is only defined '
                             'with non-negative energies')

    if centroid is None:
        centroid = spectral_centroid(y=y, sr=sr, S=S,
                                     n_fft=n_fft,
                                     hop_length=hop_length,
                                     freq=freq)

    # Compute the center frequencies of each bin
    if freq is None:
        freq = fft_frequencies(sr=sr, n_fft=n_fft)

    if freq.ndim == 1:
        deviation = np.abs(np.subtract.outer(freq, centroid[0]))
    else:
        deviation = np.abs(freq - centroid[0])

    # Column-normalize S
    if norm:
        S = util.normalize(S, norm=1, axis=0)

    return np.sum(S * deviation**p, axis=0, keepdims=True)**(1./p)
def spectral_bandwidth(y=None, sr=22050, S=None, n_fft=2048, hop_length=512,
                       win_length=None, window='hann', center=True, pad_mode='reflect',
                       freq=None, centroid=None, norm=True, p=2):
    '''Compute p'th-order spectral bandwidth:

        (sum_k S[k] * (freq[k] - centroid)**p)**(1/p)

    Parameters
    ----------
    y : np.ndarray [shape=(n,)] or None
        audio time series

    sr : number > 0 [scalar]
        audio sampling rate of `y`

    S : np.ndarray [shape=(d, t)] or None
        (optional) spectrogram magnitude

    n_fft : int > 0 [scalar]
        FFT window size

    hop_length : int > 0 [scalar]
        hop length for STFT. See `librosa.core.stft` for details.

    win_length : int <= n_fft [scalar]
        Each frame of audio is windowed by `window()`.
        The window will be of length `win_length` and then padded
        with zeros to match `n_fft`.

        If unspecified, defaults to ``win_length = n_fft``.

    window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
        - a window specification (string, tuple, or number);
          see `scipy.signal.get_window`
        - a window function, such as `scipy.signal.hanning`
        - a vector or array of length `n_fft`

        .. see also:: `filters.get_window`

    center : boolean
        - If `True`, the signal `y` is padded so that frame
          `t` is centered at `y[t * hop_length]`.
        - If `False`, then frame `t` begins at `y[t * hop_length]`

    pad_mode : string
        If `center=True`, the padding mode to use at the edges of the signal.
        By default, STFT uses reflection padding.

    freq : None or np.ndarray [shape=(d,) or shape=(d, t)]
        Center frequencies for spectrogram bins.
        If `None`, then FFT bin center frequencies are used.
        Otherwise, it can be a single array of `d` center frequencies,
        or a matrix of center frequencies as constructed by
        `librosa.core.ifgram`

    centroid : None or np.ndarray [shape=(1, t)]
        pre-computed centroid frequencies

    norm : bool
        Normalize per-frame spectral energy (sum to one)

    p : float > 0
        Power to raise deviation from spectral centroid.


    Returns
    -------
    bandwidth : np.ndarray [shape=(1, t)]
        frequency bandwidth for each frame


    Examples
    --------
    From time-series input

    >>> y, sr = librosa.load(librosa.util.example_audio_file())
    >>> spec_bw = librosa.feature.spectral_bandwidth(y=y, sr=sr)
    >>> spec_bw
    array([[ 3379.878,  1429.486, ...,  3235.214,  3080.148]])

    From spectrogram input

    >>> S, phase = librosa.magphase(librosa.stft(y=y))
    >>> librosa.feature.spectral_bandwidth(S=S)
    array([[ 3379.878,  1429.486, ...,  3235.214,  3080.148]])

    Using variable bin center frequencies

    >>> if_gram, D = librosa.ifgram(y)
    >>> librosa.feature.spectral_bandwidth(S=np.abs(D), freq=if_gram)
    array([[ 3380.011,  1429.11 , ...,  3235.22 ,  3080.148]])

    Plot the result

    >>> import matplotlib.pyplot as plt
    >>> plt.figure()
    >>> plt.subplot(2, 1, 1)
    >>> plt.semilogy(spec_bw.T, label='Spectral bandwidth')
    >>> plt.ylabel('Hz')
    >>> plt.xticks([])
    >>> plt.xlim([0, spec_bw.shape[-1]])
    >>> plt.legend()
    >>> plt.subplot(2, 1, 2)
    >>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
    ...                          y_axis='log', x_axis='time')
    >>> plt.title('log Power spectrogram')
    >>> plt.tight_layout()

    '''

    S, n_fft = _spectrogram(y=y, S=S, n_fft=n_fft, hop_length=hop_length,
                            win_length=win_length, window=window, center=center,
                            pad_mode=pad_mode)

    if not np.isrealobj(S):
        raise ParameterError('Spectral bandwidth is only defined '
                             'with real-valued input')
    elif np.any(S < 0):
        raise ParameterError('Spectral bandwidth is only defined '
                             'with non-negative energies')

    if centroid is None:
        centroid = spectral_centroid(y=y, sr=sr, S=S,
                                     n_fft=n_fft,
                                     hop_length=hop_length,
                                     freq=freq)

    # Compute the center frequencies of each bin
    if freq is None:
        freq = fft_frequencies(sr=sr, n_fft=n_fft)

    if freq.ndim == 1:
        deviation = np.abs(np.subtract.outer(freq, centroid[0]))
    else:
        deviation = np.abs(freq - centroid[0])

    # Column-normalize S
    if norm:
        S = util.normalize(S, norm=1, axis=0)

    return np.sum(S * deviation**p, axis=0, keepdims=True)**(1./p)
def spectral_bandwidth ( y = None , sr = 22050 , S = None , n_fft = 2048 , hop_length = 512 , win_length = None , window = 'hann' , center = True , pad_mode = 'reflect' , freq = None , centroid = None , norm = True , p = 2 ) : S , n_fft = _spectrogram ( y = y , S = S , n_fft = n_fft , hop_length = hop_length , win_length = win_length , window = window , center = center , pad_mode = pad_mode ) if not np . isrealobj ( S ) : raise ParameterError ( 'Spectral bandwidth is only defined ' 'with real-valued input' ) elif np . any ( S < 0 ) : raise ParameterError ( 'Spectral bandwidth is only defined ' 'with non-negative energies' ) if centroid is None : centroid = spectral_centroid ( y = y , sr = sr , S = S , n_fft = n_fft , hop_length = hop_length , freq = freq ) # Compute the center frequencies of each bin if freq is None : freq = fft_frequencies ( sr = sr , n_fft = n_fft ) if freq . ndim == 1 : deviation = np . abs ( np . subtract . outer ( freq , centroid [ 0 ] ) ) else : deviation = np . abs ( freq - centroid [ 0 ] ) # Column-normalize S if norm : S = util . normalize ( S , norm = 1 , axis = 0 ) return np . sum ( S * deviation ** p , axis = 0 , keepdims = True ) ** ( 1. / p )
Compute p'th-order spectral bandwidth:

        (sum_k S[k] * (freq[k] - centroid)**p)**(1/p)

    Parameters
    ----------
    y : np.ndarray [shape=(n,)] or None
        audio time series

    sr : number > 0 [scalar]
        audio sampling rate of `y`

    S : np.ndarray [shape=(d, t)] or None
        (optional) spectrogram magnitude

    n_fft : int > 0 [scalar]
        FFT window size

    hop_length : int > 0 [scalar]
        hop length for STFT. See `librosa.core.stft` for details.

    win_length : int <= n_fft [scalar]
        Each frame of audio is windowed by `window()`.
        The window will be of length `win_length` and then padded
        with zeros to match `n_fft`.

        If unspecified, defaults to ``win_length = n_fft``.

    window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
        - a window specification (string, tuple, or number);
          see `scipy.signal.get_window`
        - a window function, such as `scipy.signal.hanning`
        - a vector or array of length `n_fft`

        .. see also:: `filters.get_window`

    center : boolean
        - If `True`, the signal `y` is padded so that frame
          `t` is centered at `y[t * hop_length]`.
        - If `False`, then frame `t` begins at `y[t * hop_length]`

    pad_mode : string
        If `center=True`, the padding mode to use at the edges of the signal.
        By default, STFT uses reflection padding.

    freq : None or np.ndarray [shape=(d,) or shape=(d, t)]
        Center frequencies for spectrogram bins.
        If `None`, then FFT bin center frequencies are used.
        Otherwise, it can be a single array of `d` center frequencies,
        or a matrix of center frequencies as constructed by
        `librosa.core.ifgram`

    centroid : None or np.ndarray [shape=(1, t)]
        pre-computed centroid frequencies

    norm : bool
        Normalize per-frame spectral energy (sum to one)

    p : float > 0
        Power to raise deviation from spectral centroid.


    Returns
    -------
    bandwidth : np.ndarray [shape=(1, t)]
        frequency bandwidth for each frame


    Examples
    --------
    From time-series input

    >>> y, sr = librosa.load(librosa.util.example_audio_file())
    >>> spec_bw = librosa.feature.spectral_bandwidth(y=y, sr=sr)
    >>> spec_bw
    array([[ 3379.878,  1429.486, ...,  3235.214,  3080.148]])

    From spectrogram input

    >>> S, phase = librosa.magphase(librosa.stft(y=y))
    >>> librosa.feature.spectral_bandwidth(S=S)
    array([[ 3379.878,  1429.486, ...,  3235.214,  3080.148]])

    Using variable bin center frequencies

    >>> if_gram, D = librosa.ifgram(y)
    >>> librosa.feature.spectral_bandwidth(S=np.abs(D), freq=if_gram)
    array([[ 3380.011,  1429.11 , ...,  3235.22 ,  3080.148]])

    Plot the result

    >>> import matplotlib.pyplot as plt
    >>> plt.figure()
    >>> plt.subplot(2, 1, 1)
    >>> plt.semilogy(spec_bw.T, label='Spectral bandwidth')
    >>> plt.ylabel('Hz')
    >>> plt.xticks([])
    >>> plt.xlim([0, spec_bw.shape[-1]])
    >>> plt.legend()
    >>> plt.subplot(2, 1, 2)
    >>> librosa.display.specshow(librosa.amplitude_to_db(S, ref=np.max),
    ...                          y_axis='log', x_axis='time')
    >>> plt.title('log Power spectrogram')
    >>> plt.tight_layout()
Compute p th - order spectral bandwidth :