"""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
[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)