melbank.py

"""This module implements a Mel Filter Bank.
In other words it is a filter bank with triangular shaped bands
arnged on the mel frequency scale.
An example ist shown in the following figure:
.. plot::
    from pylab import plt
    import melbank
    f1, f2 = 1000, 8000
    melmat, (melfreq, fftfreq) = melbank.compute_melmat(6, f1, f2, num_fft_bands=4097)
    fig, ax = plt.subplots(figsize=(8, 3))
    ax.plot(fftfreq, melmat.T)
    ax.grid(True)
    ax.set_ylabel('Weight')
    ax.set_xlabel('Frequency / Hz')
    ax.set_xlim((f1, f2))
    ax2 = ax.twiny()
    ax2.xaxis.set_ticks_position('top')
    ax2.set_xlim((f1, f2))
    ax2.xaxis.set_ticks(melbank.mel_to_hertz(melfreq))
    ax2.xaxis.set_ticklabels(['{:.0f}'.format(mf) for mf in melfreq])
    ax2.set_xlabel('Frequency / mel')
    plt.tight_layout()
    fig, ax = plt.subplots()
    ax.matshow(melmat)
    plt.axis('equal')
    plt.axis('tight')
    plt.title('Mel Matrix')
    plt.tight_layout()
Functions
---------
"""

from numpy import abs, append, arange, insert, linspace, log10, round, zeros


def hertz_to_mel(freq):
    """Returns mel-frequency from linear frequency input.
    Parameter
    ---------
    freq : scalar or ndarray
        Frequency value or array in Hz.
    Returns
    -------
    mel : scalar or ndarray
        Mel-frequency value or ndarray in Mel
    """
    return 2595.0 * log10(1 + (freq / 700.0))


def mel_to_hertz(mel):
    """Returns frequency from mel-frequency input.
    Parameter
    ---------
    mel : scalar or ndarray
        Mel-frequency value or ndarray in Mel
    Returns
    -------
    freq : scalar or ndarray
        Frequency value or array in Hz.
    """
    return 700.0 * (10**(mel / 2595.0)) - 700.0


def melfrequencies_mel_filterbank(num_bands, freq_min, freq_max, num_fft_bands):
    """Returns centerfrequencies and band edges for a mel filter bank
    Parameters
    ----------
    num_bands : int
        Number of mel bands.
    freq_min : scalar
        Minimum frequency for the first band.
    freq_max : scalar
        Maximum frequency for the last band.
    num_fft_bands : int
        Number of fft bands.
    Returns
    -------
    center_frequencies_mel : ndarray
    lower_edges_mel : ndarray
    upper_edges_mel : ndarray
    """

    mel_max = hertz_to_mel(freq_max)
    mel_min = hertz_to_mel(freq_min)
    delta_mel = abs(mel_max - mel_min) / (num_bands + 1.0)
    frequencies_mel = mel_min + delta_mel * arange(0, num_bands + 2)
    lower_edges_mel = frequencies_mel[:-2]
    upper_edges_mel = frequencies_mel[2:]
    center_frequencies_mel = frequencies_mel[1:-1]
    return center_frequencies_mel, lower_edges_mel, upper_edges_mel


def compute_melmat(num_mel_bands=12, freq_min=64, freq_max=8000,
                   num_fft_bands=513, sample_rate=16000):
    """Returns tranformation matrix for mel spectrum.
    Parameters
    ----------
    num_mel_bands : int
        Number of mel bands. Number of rows in melmat.
        Default: 24
    freq_min : scalar
        Minimum frequency for the first band.
        Default: 64
    freq_max : scalar
        Maximum frequency for the last band.
        Default: 8000
    num_fft_bands : int
        Number of fft-frequenc bands. This ist NFFT/2+1 !
        number of columns in melmat.
        Default: 513   (this means NFFT=1024)
    sample_rate : scalar
        Sample rate for the signals that will be used.
        Default: 44100
    Returns
    -------
    melmat : ndarray
        Transformation matrix for the mel spectrum.
        Use this with fft spectra of num_fft_bands_bands length
        and multiply the spectrum with the melmat
        this will tranform your fft-spectrum
        to a mel-spectrum.
    frequencies : tuple (ndarray <num_mel_bands>, ndarray <num_fft_bands>)
        Center frequencies of the mel bands, center frequencies of fft spectrum.
    """
    center_frequencies_mel, lower_edges_mel, upper_edges_mel =  \
        melfrequencies_mel_filterbank(
            num_mel_bands,
            freq_min,
            freq_max,
            num_fft_bands
        )

    center_frequencies_hz = mel_to_hertz(center_frequencies_mel)
    lower_edges_hz = mel_to_hertz(lower_edges_mel)
    upper_edges_hz = mel_to_hertz(upper_edges_mel)
    freqs = linspace(0.0, sample_rate / 2.0, num_fft_bands)
    melmat = zeros((num_mel_bands, num_fft_bands))

    for imelband, (center, lower, upper) in enumerate(zip(
            center_frequencies_hz, lower_edges_hz, upper_edges_hz)):

        left_slope = (freqs >= lower) == (freqs <= center)
        melmat[imelband, left_slope] = (
            (freqs[left_slope] - lower) / (center - lower)
        )

        right_slope = (freqs >= center) == (freqs <= upper)
        melmat[imelband, right_slope] = (
            (upper - freqs[right_slope]) / (upper - center)
        )

    return melmat, (center_frequencies_mel, freqs)