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melbank.py
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melbank.py
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#coding: utf-8
"""
pyfilterbank is licensed unter the BSD 4-clause license:
Copyright (c) 2014, Siegfried Gündert
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. All advertising materials mentioning features or use of this software
must display the following acknowledgement:
This product includes software developed by the <organization>.
4. Neither the name of the <organization> nor the
names of its contributors may be used to endorse or promote products
derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY <COPYRIGHT HOLDER> ''AS IS'' AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
"""
"""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
)
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)
if __name__ == '__main__':
from pylab import plt
# num_banks=300 need more num_fft_banks
f1, f2, num_banks, num_fft_bands, sample_rate= 50, 8000, 100, (1024*2/2)+1, 22000
melmat, (melfreq, fftfreq) = compute_melmat(num_banks, f1, f2, num_fft_bands, sample_rate)
#print melmat[0,:]
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(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()
plt.show()