librosa/filters.py
def mel(sr, n_fft, n_mels=128, fmin=0.0, fmax=None, htk=False,
        norm=1, dtype=np.float32):
    """Create a Filterbank matrix to combine FFT bins into Mel-frequency bins

    Parameters
    ----------
    sr        : number > 0 [scalar]
        sampling rate of the incoming signal

    n_fft     : int > 0 [scalar]
        number of FFT components

    n_mels    : int > 0 [scalar]
        number of Mel bands to generate

    fmin      : float >= 0 [scalar]
        lowest frequency (in Hz)

    fmax      : float >= 0 [scalar]
        highest frequency (in Hz).
        If `None`, use `fmax = sr / 2.0`

    htk       : bool [scalar]
        use HTK formula instead of Slaney

    norm : {None, 1, np.inf} [scalar]
        if 1, divide the triangular mel weights by the width of the mel band
        (area normalization).  Otherwise, leave all the triangles aiming for
        a peak value of 1.0

    dtype : np.dtype
        The data type of the output basis.
        By default, uses 32-bit (single-precision) floating point.

    Returns
    -------
    M         : np.ndarray [shape=(n_mels, 1 + n_fft/2)]
        Mel transform matrix

    Notes
    -----
    This function caches at level 10.

    Examples
    --------
    >>> melfb = librosa.filters.mel(22050, 2048)
    >>> melfb
    array([[ 0.   ,  0.016, ...,  0.   ,  0.   ],
           [ 0.   ,  0.   , ...,  0.   ,  0.   ],
           ...,
           [ 0.   ,  0.   , ...,  0.   ,  0.   ],
           [ 0.   ,  0.   , ...,  0.   ,  0.   ]])


    Clip the maximum frequency to 8KHz

    >>> librosa.filters.mel(22050, 2048, fmax=8000)
    array([[ 0.  ,  0.02, ...,  0.  ,  0.  ],
           [ 0.  ,  0.  , ...,  0.  ,  0.  ],
           ...,
           [ 0.  ,  0.  , ...,  0.  ,  0.  ],
           [ 0.  ,  0.  , ...,  0.  ,  0.  ]])


    >>> import matplotlib.pyplot as plt
    >>> plt.figure()
    >>> librosa.display.specshow(melfb, x_axis='linear')
    >>> plt.ylabel('Mel filter')
    >>> plt.title('Mel filter bank')
    >>> plt.colorbar()
    >>> plt.tight_layout()
    """

    if fmax is None:
        fmax = float(sr) / 2

    if norm is not None and norm != 1 and norm != np.inf:
        raise ParameterError('Unsupported norm: {}'.format(repr(norm)))

    # Initialize the weights
    n_mels = int(n_mels)
    weights = np.zeros((n_mels, int(1 + n_fft // 2)), dtype=dtype)

    # Center freqs of each FFT bin
    fftfreqs = fft_frequencies(sr=sr, n_fft=n_fft)

    # 'Center freqs' of mel bands - uniformly spaced between limits
    mel_f = mel_frequencies(n_mels + 2, fmin=fmin, fmax=fmax, htk=htk)

    fdiff = np.diff(mel_f)
    ramps = np.subtract.outer(mel_f, fftfreqs)

    for i in range(n_mels):
        # lower and upper slopes for all bins
        lower = -ramps[i] / fdiff[i]
        upper = ramps[i+2] / fdiff[i+1]

        # .. then intersect them with each other and zero
        weights[i] = np.maximum(0, np.minimum(lower, upper))

    if norm == 1:
        # Slaney-style mel is scaled to be approx constant energy per channel
        enorm = 2.0 / (mel_f[2:n_mels+2] - mel_f[:n_mels])
        weights *= enorm[:, np.newaxis]

    # Only check weights if f_mel[0] is positive
    if not np.all((mel_f[:-2] == 0) | (weights.max(axis=1) > 0)):
        # This means we have an empty channel somewhere
        warnings.warn('Empty filters detected in mel frequency basis. '
                      'Some channels will produce empty responses. '
                      'Try increasing your sampling rate (and fmax) or '
                      'reducing n_mels.')

    return weights
def mel(sr, n_fft, n_mels=128, fmin=0.0, fmax=None, htk=False,
        norm=1, dtype=np.float32):
    """Create a Filterbank matrix to combine FFT bins into Mel-frequency bins

    Parameters
    ----------
    sr        : number > 0 [scalar]
        sampling rate of the incoming signal

    n_fft     : int > 0 [scalar]
        number of FFT components

    n_mels    : int > 0 [scalar]
        number of Mel bands to generate

    fmin      : float >= 0 [scalar]
        lowest frequency (in Hz)

    fmax      : float >= 0 [scalar]
        highest frequency (in Hz).
        If `None`, use `fmax = sr / 2.0`

    htk       : bool [scalar]
        use HTK formula instead of Slaney

    norm : {None, 1, np.inf} [scalar]
        if 1, divide the triangular mel weights by the width of the mel band
        (area normalization).  Otherwise, leave all the triangles aiming for
        a peak value of 1.0

    dtype : np.dtype
        The data type of the output basis.
        By default, uses 32-bit (single-precision) floating point.

    Returns
    -------
    M         : np.ndarray [shape=(n_mels, 1 + n_fft/2)]
        Mel transform matrix

    Notes
    -----
    This function caches at level 10.

    Examples
    --------
    >>> melfb = librosa.filters.mel(22050, 2048)
    >>> melfb
    array([[ 0.   ,  0.016, ...,  0.   ,  0.   ],
           [ 0.   ,  0.   , ...,  0.   ,  0.   ],
           ...,
           [ 0.   ,  0.   , ...,  0.   ,  0.   ],
           [ 0.   ,  0.   , ...,  0.   ,  0.   ]])


    Clip the maximum frequency to 8KHz

    >>> librosa.filters.mel(22050, 2048, fmax=8000)
    array([[ 0.  ,  0.02, ...,  0.  ,  0.  ],
           [ 0.  ,  0.  , ...,  0.  ,  0.  ],
           ...,
           [ 0.  ,  0.  , ...,  0.  ,  0.  ],
           [ 0.  ,  0.  , ...,  0.  ,  0.  ]])


    >>> import matplotlib.pyplot as plt
    >>> plt.figure()
    >>> librosa.display.specshow(melfb, x_axis='linear')
    >>> plt.ylabel('Mel filter')
    >>> plt.title('Mel filter bank')
    >>> plt.colorbar()
    >>> plt.tight_layout()
    """

    if fmax is None:
        fmax = float(sr) / 2

    if norm is not None and norm != 1 and norm != np.inf:
        raise ParameterError('Unsupported norm: {}'.format(repr(norm)))

    # Initialize the weights
    n_mels = int(n_mels)
    weights = np.zeros((n_mels, int(1 + n_fft // 2)), dtype=dtype)

    # Center freqs of each FFT bin
    fftfreqs = fft_frequencies(sr=sr, n_fft=n_fft)

    # 'Center freqs' of mel bands - uniformly spaced between limits
    mel_f = mel_frequencies(n_mels + 2, fmin=fmin, fmax=fmax, htk=htk)

    fdiff = np.diff(mel_f)
    ramps = np.subtract.outer(mel_f, fftfreqs)

    for i in range(n_mels):
        # lower and upper slopes for all bins
        lower = -ramps[i] / fdiff[i]
        upper = ramps[i+2] / fdiff[i+1]

        # .. then intersect them with each other and zero
        weights[i] = np.maximum(0, np.minimum(lower, upper))

    if norm == 1:
        # Slaney-style mel is scaled to be approx constant energy per channel
        enorm = 2.0 / (mel_f[2:n_mels+2] - mel_f[:n_mels])
        weights *= enorm[:, np.newaxis]

    # Only check weights if f_mel[0] is positive
    if not np.all((mel_f[:-2] == 0) | (weights.max(axis=1) > 0)):
        # This means we have an empty channel somewhere
        warnings.warn('Empty filters detected in mel frequency basis. '
                      'Some channels will produce empty responses. '
                      'Try increasing your sampling rate (and fmax) or '
                      'reducing n_mels.')

    return weights
Create a Filterbank matrix to combine FFT bins into Mel-frequency bins

    Parameters
    ----------
    sr        : number > 0 [scalar]
        sampling rate of the incoming signal

    n_fft     : int > 0 [scalar]
        number of FFT components

    n_mels    : int > 0 [scalar]
        number of Mel bands to generate

    fmin      : float >= 0 [scalar]
        lowest frequency (in Hz)

    fmax      : float >= 0 [scalar]
        highest frequency (in Hz).
        If `None`, use `fmax = sr / 2.0`

    htk       : bool [scalar]
        use HTK formula instead of Slaney

    norm : {None, 1, np.inf} [scalar]
        if 1, divide the triangular mel weights by the width of the mel band
        (area normalization).  Otherwise, leave all the triangles aiming for
        a peak value of 1.0

    dtype : np.dtype
        The data type of the output basis.
        By default, uses 32-bit (single-precision) floating point.

    Returns
    -------
    M         : np.ndarray [shape=(n_mels, 1 + n_fft/2)]
        Mel transform matrix

    Notes
    -----
    This function caches at level 10.

    Examples
    --------
    >>> melfb = librosa.filters.mel(22050, 2048)
    >>> melfb
    array([[ 0.   ,  0.016, ...,  0.   ,  0.   ],
           [ 0.   ,  0.   , ...,  0.   ,  0.   ],
           ...,
           [ 0.   ,  0.   , ...,  0.   ,  0.   ],
           [ 0.   ,  0.   , ...,  0.   ,  0.   ]])


    Clip the maximum frequency to 8KHz

    >>> librosa.filters.mel(22050, 2048, fmax=8000)
    array([[ 0.  ,  0.02, ...,  0.  ,  0.  ],
           [ 0.  ,  0.  , ...,  0.  ,  0.  ],
           ...,
           [ 0.  ,  0.  , ...,  0.  ,  0.  ],
           [ 0.  ,  0.  , ...,  0.  ,  0.  ]])


    >>> import matplotlib.pyplot as plt
    >>> plt.figure()
    >>> librosa.display.specshow(melfb, x_axis='linear')
    >>> plt.ylabel('Mel filter')
    >>> plt.title('Mel filter bank')
    >>> plt.colorbar()
    >>> plt.tight_layout()