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MFCCs Extraction in Python

An important feature we often use in Speech Analysis is Mel-Frequency Cepstral Coefficients(MFCC).

0x01 What’s MFCCs?

  • A ppt from Carnegie Mellon University
  • wiki

0x02 How to extract?

steps:

Here are codes from python_speech_features, very nice and worth reading.

sigproc.py

# This file includes routines for basic signal processing including framing and computing power spectra.
# Author: James Lyons 2012
import decimal

import numpy
import math
import logging

def round_half_up(number):
    return int(decimal.Decimal(number).quantize(decimal.Decimal('1'), rounding=decimal.ROUND_HALF_UP))


def framesig(sig,frame_len,frame_step,winfunc=lambda x:numpy.ones((x,))):
    """Frame a signal into overlapping frames.
    :param sig: the audio signal to frame.
    :param frame_len: length of each frame measured in samples.
    :param frame_step: number of samples after the start of the previous frame that the next frame should begin.
    :param winfunc: the analysis window to apply to each frame. By default no window is applied.
    :returns: an array of frames. Size is NUMFRAMES by frame_len.
    """
    slen = len(sig)
    frame_len = int(round_half_up(frame_len))
    frame_step = int(round_half_up(frame_step))
    if slen <= frame_len:
        numframes = 1
    else:
        numframes = 1 + int(math.ceil((1.0*slen - frame_len)/frame_step))

    padlen = int((numframes-1)*frame_step + frame_len)

    zeros = numpy.zeros((padlen - slen,))
    padsignal = numpy.concatenate((sig,zeros))

    indices = numpy.tile(numpy.arange(0,frame_len),(numframes,1)) + numpy.tile(numpy.arange(0,numframes*frame_step,frame_step),(frame_len,1)).T
    indices = numpy.array(indices,dtype=numpy.int32)
    frames = padsignal[indices]
    win = numpy.tile(winfunc(frame_len),(numframes,1))
    return frames*win


def deframesig(frames,siglen,frame_len,frame_step,winfunc=lambda x:numpy.ones((x,))):
    """Does overlap-add procedure to undo the action of framesig.
    :param frames: the array of frames.
    :param siglen: the length of the desired signal, use 0 if unknown. Output will be truncated to siglen samples.
    :param frame_len: length of each frame measured in samples.
    :param frame_step: number of samples after the start of the previous frame that the next frame should begin.
    :param winfunc: the analysis window to apply to each frame. By default no window is applied.
    :returns: a 1-D signal.
    """
    frame_len = round_half_up(frame_len)
    frame_step = round_half_up(frame_step)
    numframes = numpy.shape(frames)[0]
    assert numpy.shape(frames)[1] == frame_len, '"frames" matrix is wrong size, 2nd dim is not equal to frame_len'

    indices = numpy.tile(numpy.arange(0,frame_len),(numframes,1)) + numpy.tile(numpy.arange(0,numframes*frame_step,frame_step),(frame_len,1)).T
    indices = numpy.array(indices,dtype=numpy.int32)
    padlen = (numframes-1)*frame_step + frame_len   

    if siglen <= 0: siglen = padlen

    rec_signal = numpy.zeros((padlen,))
    window_correction = numpy.zeros((padlen,))
    win = winfunc(frame_len)

    for i in range(0,numframes):
        window_correction[indices[i,:]] = window_correction[indices[i,:]] + win + 1e-15 #add a little bit so it is never zero
        rec_signal[indices[i,:]] = rec_signal[indices[i,:]] + frames[i,:]

    rec_signal = rec_signal/window_correction
    return rec_signal[0:siglen]

def magspec(frames,NFFT):
    """Compute the magnitude spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1). 
    :param frames: the array of frames. Each row is a frame.
    :param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded. 
    :returns: If frames is an NxD matrix, output will be Nx(NFFT/2+1). Each row will be the magnitude spectrum of the corresponding frame.
    """    
    if numpy.shape(frames)[1] > NFFT: 
        logging.warn('frame length (%d) is greater than FFT size (%d), frame will be truncated. Increase NFFT to avoid.', numpy.shape(frames)[1], NFFT)
    complex_spec = numpy.fft.rfft(frames,NFFT)
    return numpy.absolute(complex_spec)

def powspec(frames,NFFT):
    """Compute the power spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1). 
    :param frames: the array of frames. Each row is a frame.
    :param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded. 
    :returns: If frames is an NxD matrix, output will be Nx(NFFT/2+1). Each row will be the power spectrum of the corresponding frame.
    """    
    return 1.0/NFFT * numpy.square(magspec(frames,NFFT))

def logpowspec(frames,NFFT,norm=1):
    """Compute the log power spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1). 
    :param frames: the array of frames. Each row is a frame.
    :param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded. 
    :param norm: If norm=1, the log power spectrum is normalised so that the max value (across all frames) is 0.
    :returns: If frames is an NxD matrix, output will be Nx(NFFT/2+1). Each row will be the log power spectrum of the corresponding frame.
    """    
    ps = powspec(frames,NFFT);
    ps[ps<=1e-30] = 1e-30
    lps = 10*numpy.log10(ps)
    if norm:
        return lps - numpy.max(lps)
    else:
        return lps

def preemphasis(signal,coeff=0.95):
    """perform preemphasis on the input signal.

    :param signal: The signal to filter.
    :param coeff: The preemphasis coefficient. 0 is no filter, default is 0.95.
    :returns: the filtered signal.
    """    
    return numpy.append(signal[0],signal[1:]-coeff*signal[:-1])

compute.py

import numpy
import sigproc
from scipy.fftpack import dct

def mfcc(signal,samplerate=16000,winlen=0.025,winstep=0.01,numcep=13,
         nfilt=26,nfft=512,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 samplerate of the signal we are working with.
    :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 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 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.
    :returns: A numpy array of size (NUMFRAMES by numcep) containing features. Each row holds 1 feature vector.
    """            
    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 samplerate of the signal we are working with.
    :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.
    :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):
    """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 samplerate of the signal we are working with.
    :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. 
    :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)
    return numpy.log(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 samplerate of the signal we are working with. 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

In fact I will use Librosa in my project, it’s more powerful and elegant :P

Example: http://musicinformationretrieval.com/mfcc.html