155 lines
4.9 KiB
Python
155 lines
4.9 KiB
Python
"""This module implements a Mel Filter Bank.
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In other words it is a filter bank with triangular shaped bands
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arnged on the mel frequency scale.
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An example ist shown in the following figure:
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.. plot::
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from pylab import plt
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import melbank
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f1, f2 = 1000, 8000
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melmat, (melfreq, fftfreq) = melbank.compute_melmat(6, f1, f2, num_fft_bands=4097)
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fig, ax = plt.subplots(figsize=(8, 3))
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ax.plot(fftfreq, melmat.T)
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ax.grid(True)
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ax.set_ylabel('Weight')
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ax.set_xlabel('Frequency / Hz')
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ax.set_xlim((f1, f2))
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ax2 = ax.twiny()
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ax2.xaxis.set_ticks_position('top')
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ax2.set_xlim((f1, f2))
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ax2.xaxis.set_ticks(melbank.mel_to_hertz(melfreq))
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ax2.xaxis.set_ticklabels(['{:.0f}'.format(mf) for mf in melfreq])
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ax2.set_xlabel('Frequency / mel')
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plt.tight_layout()
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fig, ax = plt.subplots()
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ax.matshow(melmat)
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plt.axis('equal')
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plt.axis('tight')
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plt.title('Mel Matrix')
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plt.tight_layout()
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Functions
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---------
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"""
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from numpy import abs, append, arange, insert, linspace, log10, round, zeros
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from math import log
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def hertz_to_mel(freq):
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"""Returns mel-frequency from linear frequency input.
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Parameter
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---------
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freq : scalar or ndarray
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Frequency value or array in Hz.
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Returns
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-------
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mel : scalar or ndarray
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Mel-frequency value or ndarray in Mel
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"""
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#return 2595.0 * log10(1 + (freq / 700.0))
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return 3340.0 * log(1 + (freq / 250.0), 9)
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def mel_to_hertz(mel):
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"""Returns frequency from mel-frequency input.
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Parameter
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---------
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mel : scalar or ndarray
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Mel-frequency value or ndarray in Mel
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Returns
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-------
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freq : scalar or ndarray
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Frequency value or array in Hz.
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"""
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#return 700.0 * (10**(mel / 2595.0)) - 700.0
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return 250.0 * (9**(mel / 3340.0)) - 250.0
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def melfrequencies_mel_filterbank(num_bands, freq_min, freq_max, num_fft_bands):
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"""Returns centerfrequencies and band edges for a mel filter bank
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Parameters
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----------
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num_bands : int
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Number of mel bands.
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freq_min : scalar
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Minimum frequency for the first band.
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freq_max : scalar
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Maximum frequency for the last band.
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num_fft_bands : int
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Number of fft bands.
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Returns
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-------
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center_frequencies_mel : ndarray
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lower_edges_mel : ndarray
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upper_edges_mel : ndarray
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"""
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mel_max = hertz_to_mel(freq_max)
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mel_min = hertz_to_mel(freq_min)
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delta_mel = abs(mel_max - mel_min) / (num_bands + 1.0)
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frequencies_mel = mel_min + delta_mel * arange(0, num_bands + 2)
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lower_edges_mel = frequencies_mel[:-2]
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upper_edges_mel = frequencies_mel[2:]
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center_frequencies_mel = frequencies_mel[1:-1]
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return center_frequencies_mel, lower_edges_mel, upper_edges_mel
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def compute_melmat(num_mel_bands=12, freq_min=64, freq_max=8000,
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num_fft_bands=513, sample_rate=16000):
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"""Returns tranformation matrix for mel spectrum.
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Parameters
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----------
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num_mel_bands : int
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Number of mel bands. Number of rows in melmat.
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Default: 24
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freq_min : scalar
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Minimum frequency for the first band.
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Default: 64
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freq_max : scalar
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Maximum frequency for the last band.
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Default: 8000
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num_fft_bands : int
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Number of fft-frequenc bands. This ist NFFT/2+1 !
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number of columns in melmat.
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Default: 513 (this means NFFT=1024)
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sample_rate : scalar
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Sample rate for the signals that will be used.
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Default: 44100
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Returns
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-------
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melmat : ndarray
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Transformation matrix for the mel spectrum.
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Use this with fft spectra of num_fft_bands_bands length
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and multiply the spectrum with the melmat
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this will tranform your fft-spectrum
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to a mel-spectrum.
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frequencies : tuple (ndarray <num_mel_bands>, ndarray <num_fft_bands>)
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Center frequencies of the mel bands, center frequencies of fft spectrum.
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"""
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center_frequencies_mel, lower_edges_mel, upper_edges_mel = \
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melfrequencies_mel_filterbank(
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num_mel_bands,
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freq_min,
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freq_max,
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num_fft_bands
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)
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center_frequencies_hz = mel_to_hertz(center_frequencies_mel)
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lower_edges_hz = mel_to_hertz(lower_edges_mel)
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upper_edges_hz = mel_to_hertz(upper_edges_mel)
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freqs = linspace(0.0, sample_rate / 2.0, num_fft_bands)
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melmat = zeros((num_mel_bands, num_fft_bands))
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for imelband, (center, lower, upper) in enumerate(zip(
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center_frequencies_hz, lower_edges_hz, upper_edges_hz)):
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left_slope = (freqs >= lower) == (freqs <= center)
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melmat[imelband, left_slope] = (
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(freqs[left_slope] - lower) / (center - lower)
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)
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right_slope = (freqs >= center) == (freqs <= upper)
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melmat[imelband, right_slope] = (
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(upper - freqs[right_slope]) / (upper - center)
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)
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return melmat, (center_frequencies_mel, freqs)
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