Source code for melbank

"""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.set_xlabel('Frequency / Hz')
    ax.set_xlim((f1, f2))
    ax2 = ax.twiny()
    ax2.set_xlim((f1, f2))
    ax2.xaxis.set_ticklabels(['{:.0f}'.format(mf) for mf in melfreq])
    ax2.set_xlabel('Frequency / mel')

    fig, ax = plt.subplots()
    plt.title('Mel Matrix')


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

[docs]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))
[docs]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
[docs]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
[docs]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 ) len_fft = float(num_fft_bands) / sample_rate 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)