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# calculate filterbank features. Provides e.g. fbank and mfcc features for use in ASR applications
# Author: James Lyons 2012
from __future__ import division
import numpy
from python_speech_features import sigproc
from scipy.fftpack import dct
def calculate_nfft(samplerate, winlen):
"""Calculates the FFT size as a power of two greater than or equal to
the number of samples in a single window length.
Having an FFT less than the window length loses precision by dropping
many of the samples; a longer FFT than the window allows zero-padding
of the FFT buffer which is neutral in terms of frequency domain conversion.
:param samplerate: The sample rate of the signal we are working with, in Hz.
:param winlen: The length of the analysis window in seconds.
"""
window_length_samples = winlen * samplerate
nfft = 1
while nfft < window_length_samples:
nfft *= 2
return nfft
def mfcc(signal,samplerate=16000,winlen=0.025,winstep=0.01,numcep=13,
nfilt=26,nfft=None,lowfreq=0,highfreq=None,preemph=0.97,ceplifter=22,appendEnergy=True,
winfunc=lambda x:numpy.ones((x,))):
"""Compute MFCC features from an audio signal.
:param signal: the audio signal from which to compute features. Should be an N*1 array
:param samplerate: the sample rate of the signal we are working with, in Hz.
:param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
:param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
:param numcep: the number of cepstrum to return, default 13
:param nfilt: the number of filters in the filterbank, default 26.
:param nfft: the FFT size. Default is None, which uses the calculate_nfft function to choose the smallest size that does not drop sample data.
:param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
:param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
:param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
:param ceplifter: apply a lifter to final cepstral coefficients. 0 is no lifter. Default is 22.
:param appendEnergy: if this is true, the zeroth cepstral coefficient is replaced with the log of the total frame energy.
:param winfunc: the analysis window to apply to each frame. By default no window is applied. You can use numpy window functions here e.g. winfunc=numpy.hamming
:returns: A numpy array of size (NUMFRAMES by numcep) containing features. Each row holds 1 feature vector.
"""
nfft = nfft or calculate_nfft(samplerate, winlen)
feat,energy = fbank(signal,samplerate,winlen,winstep,nfilt,nfft,lowfreq,highfreq,preemph,winfunc)
feat = numpy.log(feat)
feat = dct(feat, type=2, axis=1, norm='ortho')[:,:numcep]
feat = lifter(feat,ceplifter)
if appendEnergy: feat[:,0] = numpy.log(energy) # replace first cepstral coefficient with log of frame energy
return feat
def fbank(signal,samplerate=16000,winlen=0.025,winstep=0.01,
nfilt=26,nfft=512,lowfreq=0,highfreq=None,preemph=0.97,
winfunc=lambda x:numpy.ones((x,))):
"""Compute Mel-filterbank energy features from an audio signal.
:param signal: the audio signal from which to compute features. Should be an N*1 array
:param samplerate: the sample rate of the signal we are working with, in Hz.
:param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
:param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
:param nfilt: the number of filters in the filterbank, default 26.
:param nfft: the FFT size. Default is 512.
:param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
:param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
:param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
:param winfunc: the analysis window to apply to each frame. By default no window is applied. You can use numpy window functions here e.g. winfunc=numpy.hamming
:returns: 2 values. The first is a numpy array of size (NUMFRAMES by nfilt) containing features. Each row holds 1 feature vector. The
second return value is the energy in each frame (total energy, unwindowed)
"""
highfreq= highfreq or samplerate/2
signal = sigproc.preemphasis(signal,preemph)
frames = sigproc.framesig(signal, winlen*samplerate, winstep*samplerate, winfunc)
pspec = sigproc.powspec(frames,nfft)
energy = numpy.sum(pspec,1) # this stores the total energy in each frame
energy = numpy.where(energy == 0,numpy.finfo(float).eps,energy) # if energy is zero, we get problems with log
fb = get_filterbanks(nfilt,nfft,samplerate,lowfreq,highfreq)
feat = numpy.dot(pspec,fb.T) # compute the filterbank energies
feat = numpy.where(feat == 0,numpy.finfo(float).eps,feat) # if feat is zero, we get problems with log
return feat,energy
def logfbank(signal,samplerate=16000,winlen=0.025,winstep=0.01,
nfilt=26,nfft=512,lowfreq=0,highfreq=None,preemph=0.97,
winfunc=lambda x:numpy.ones((x,))):
"""Compute log Mel-filterbank energy features from an audio signal.
:param signal: the audio signal from which to compute features. Should be an N*1 array
:param samplerate: the sample rate of the signal we are working with, in Hz.
:param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
:param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
:param nfilt: the number of filters in the filterbank, default 26.
:param nfft: the FFT size. Default is 512.
:param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
:param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
:param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
:param winfunc: the analysis window to apply to each frame. By default no window is applied. You can use numpy window functions here e.g. winfunc=numpy.hamming
:returns: A numpy array of size (NUMFRAMES by nfilt) containing features. Each row holds 1 feature vector.
"""
feat,energy = fbank(signal,samplerate,winlen,winstep,nfilt,nfft,lowfreq,highfreq,preemph,winfunc)
return numpy.log(feat)
def ssc(signal,samplerate=16000,winlen=0.025,winstep=0.01,
nfilt=26,nfft=512,lowfreq=0,highfreq=None,preemph=0.97,
winfunc=lambda x:numpy.ones((x,))):
"""Compute Spectral Subband Centroid features from an audio signal.
:param signal: the audio signal from which to compute features. Should be an N*1 array
:param samplerate: the sample rate of the signal we are working with, in Hz.
:param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
:param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
:param nfilt: the number of filters in the filterbank, default 26.
:param nfft: the FFT size. Default is 512.
:param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
:param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
:param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
:param winfunc: the analysis window to apply to each frame. By default no window is applied. You can use numpy window functions here e.g. winfunc=numpy.hamming
:returns: A numpy array of size (NUMFRAMES by nfilt) containing features. Each row holds 1 feature vector.
"""
highfreq= highfreq or samplerate/2
signal = sigproc.preemphasis(signal,preemph)
frames = sigproc.framesig(signal, winlen*samplerate, winstep*samplerate, winfunc)
pspec = sigproc.powspec(frames,nfft)
pspec = numpy.where(pspec == 0,numpy.finfo(float).eps,pspec) # if things are all zeros we get problems
fb = get_filterbanks(nfilt,nfft,samplerate,lowfreq,highfreq)
feat = numpy.dot(pspec,fb.T) # compute the filterbank energies
R = numpy.tile(numpy.linspace(1,samplerate/2,numpy.size(pspec,1)),(numpy.size(pspec,0),1))
return numpy.dot(pspec*R,fb.T) / feat
def hz2mel(hz):
"""Convert a value in Hertz to Mels
:param hz: a value in Hz. This can also be a numpy array, conversion proceeds element-wise.
:returns: a value in Mels. If an array was passed in, an identical sized array is returned.
"""
return 2595 * numpy.log10(1+hz/700.)
def mel2hz(mel):
"""Convert a value in Mels to Hertz
:param mel: a value in Mels. This can also be a numpy array, conversion proceeds element-wise.
:returns: a value in Hertz. If an array was passed in, an identical sized array is returned.
"""
return 700*(10**(mel/2595.0)-1)
def get_filterbanks(nfilt=20,nfft=512,samplerate=16000,lowfreq=0,highfreq=None):
"""Compute a Mel-filterbank. The filters are stored in the rows, the columns correspond
to fft bins. The filters are returned as an array of size nfilt * (nfft/2 + 1)
:param nfilt: the number of filters in the filterbank, default 20.
:param nfft: the FFT size. Default is 512.
:param samplerate: the sample rate of the signal we are working with, in Hz. Affects mel spacing.
:param lowfreq: lowest band edge of mel filters, default 0 Hz
:param highfreq: highest band edge of mel filters, default samplerate/2
:returns: A numpy array of size nfilt * (nfft/2 + 1) containing filterbank. Each row holds 1 filter.
"""
highfreq= highfreq or samplerate/2
assert highfreq <= samplerate/2, "highfreq is greater than samplerate/2"
# compute points evenly spaced in mels
lowmel = hz2mel(lowfreq)
highmel = hz2mel(highfreq)
melpoints = numpy.linspace(lowmel,highmel,nfilt+2)
# our points are in Hz, but we use fft bins, so we have to convert
# from Hz to fft bin number
bin = numpy.floor((nfft+1)*mel2hz(melpoints)/samplerate)
fbank = numpy.zeros([nfilt,nfft//2+1])
for j in range(0,nfilt):
for i in range(int(bin[j]), int(bin[j+1])):
fbank[j,i] = (i - bin[j]) / (bin[j+1]-bin[j])
for i in range(int(bin[j+1]), int(bin[j+2])):
fbank[j,i] = (bin[j+2]-i) / (bin[j+2]-bin[j+1])
return fbank
def lifter(cepstra, L=22):
"""Apply a cepstral lifter the the matrix of cepstra. This has the effect of increasing the
magnitude of the high frequency DCT coeffs.
:param cepstra: the matrix of mel-cepstra, will be numframes * numcep in size.
:param L: the liftering coefficient to use. Default is 22. L <= 0 disables lifter.
"""
if L > 0:
nframes,ncoeff = numpy.shape(cepstra)
n = numpy.arange(ncoeff)
lift = 1 + (L/2.)*numpy.sin(numpy.pi*n/L)
return lift*cepstra
else:
# values of L <= 0, do nothing
return cepstra
def delta(feat, N):
"""Compute delta features from a feature vector sequence.
:param feat: A numpy array of size (NUMFRAMES by number of features) containing features. Each row holds 1 feature vector.
:param N: For each frame, calculate delta features based on preceding and following N frames
:returns: A numpy array of size (NUMFRAMES by number of features) containing delta features. Each row holds 1 delta feature vector.
"""
if N < 1:
raise ValueError('N must be an integer >= 1')
NUMFRAMES = len(feat)
denominator = 2 * sum([i**2 for i in range(1, N+1)])
delta_feat = numpy.empty_like(feat)
padded = numpy.pad(feat, ((N, N), (0, 0)), mode='edge') # padded version of feat
for t in range(NUMFRAMES):
delta_feat[t] = numpy.dot(numpy.arange(-N, N+1), padded[t : t+2*N+1]) / denominator # [t : t+2*N+1] == [(N+t)-N : (N+t)+N+1]
return delta_feat