mfcc.py

# Copyright (c) 2006 Carnegie Mellon University
#
# You may copy and modify this freely under the same terms as
# Sphinx-III
# 
# Source : http://www.cs.cmu.edu/%7Edhuggins/Projects/pyphone/sphinx/mfcc.py
#

"""Compute MFCC coefficients.

This module provides functions for computing MFCC (mel-frequency
cepstral coefficients) as used in the Sphinx speech recognition
system.
"""

__author__ = "David Huggins-Daines <dhuggins@cs.cmu.edu>"
__version__ = "$Revision: 6390 $"

import numpy, numpy.fft

def mel(f):
    return 2595. * numpy.log10(1. + f / 700.)

def melinv(m):
    return 700. * (numpy.power(10., m / 2595.) - 1.)

class MFCC(object):
    def __init__(self, nfilt=40, ncep=13,
                 lowerf=133.3333, upperf=6855.4976, alpha=0.97,
                 samprate=16000, frate=100, wlen=0.0256,
                 nfft=512):
        # Store parameters
        self.lowerf = lowerf
        self.upperf = upperf
        self.nfft = nfft
        self.ncep = ncep
        self.nfilt = nfilt
        self.frate = frate
        self.fshift = float(samprate) / frate

        # Build Hamming window
        self.wlen = int(wlen * samprate)
        self.win = numpy.hamming(self.wlen)

        # Prior sample for pre-emphasis
        self.prior = 0
        self.alpha = alpha

        # Build mel filter matrix
        self.filters = numpy.zeros((nfft/2+1,nfilt), 'd')
        dfreq = float(samprate) / nfft
        if upperf > samprate/2:
            raise(Exception,
                   "Upper frequency %f exceeds Nyquist %f" % (upperf, samprate/2))
        melmax = mel(upperf)
        melmin = mel(lowerf)
        dmelbw = (melmax - melmin) / (nfilt + 1)
        # Filter edges, in Hz
        filt_edge = melinv(melmin + dmelbw * numpy.arange(nfilt + 2, dtype='d'))

        for whichfilt in range(0, nfilt):
            # Filter triangles, in DFT points
            leftfr = round(filt_edge[whichfilt] / dfreq)
            centerfr = round(filt_edge[whichfilt + 1] / dfreq)
            rightfr = round(filt_edge[whichfilt + 2] / dfreq)
            # For some reason this is calculated in Hz, though I think
            # it doesn't really matter
            fwidth = (rightfr - leftfr) * dfreq
            height = 2. / fwidth

            if centerfr != leftfr:
                leftslope = height / (centerfr - leftfr)
            else:
                leftslope = 0
            freq = leftfr + 1
            while freq < centerfr:
                self.filters[freq,whichfilt] = (freq - leftfr) * leftslope
                freq = freq + 1
            if freq == centerfr: # This is always true
                self.filters[freq,whichfilt] = height
                freq = freq + 1
            if centerfr != rightfr:
                rightslope = height / (centerfr - rightfr)
            while freq < rightfr:
                self.filters[freq,whichfilt] = (freq - rightfr) * rightslope
                freq = freq + 1
#             print("Filter %d: left %d=%f center %d=%f right %d=%f width %d" %
#                   (whichfilt,
#                   leftfr, leftfr*dfreq,
#                   centerfr, centerfr*dfreq,
#                   rightfr, rightfr*dfreq,
#                   freq - leftfr))
#             print self.filters[leftfr:rightfr,whichfilt]

        # Build DCT matrix
        self.s2dct = s2dctmat(nfilt, ncep, 1./nfilt)
        self.dct = dctmat(nfilt, ncep, numpy.pi/nfilt)

    def sig2s2mfc(self, sig):
        nfr = int(len(sig) / self.fshift + 1)
        mfcc = numpy.zeros((nfr, self.ncep), 'd')
        fr = 0
        while fr < nfr:
            start = round(fr * self.fshift)
            end = min(len(sig), start + self.wlen)
            frame = sig[start:end]
            if len(frame) < self.wlen:
                frame = numpy.resize(frame,self.wlen)
                frame[self.wlen:] = 0
            mfcc[fr] = self.frame2s2mfc(frame)
            fr = fr + 1
        return mfcc

    def sig2logspec(self, sig):
        nfr = int(len(sig) / self.fshift + 1)
        mfcc = numpy.zeros((nfr, self.nfilt), 'd')
        fr = 0
        while fr < nfr:
            start = round(fr * self.fshift)
            end = min(len(sig), start + self.wlen)
            frame = sig[start:end]
            if len(frame) < self.wlen:
                frame = numpy.resize(frame,self.wlen)
                frame[self.wlen:] = 0
            mfcc[fr] = self.frame2logspec(frame)
            fr = fr + 1
        return mfcc

    def pre_emphasis(self, frame):
        # FIXME: Do this with matrix multiplication
        outfr = numpy.empty(len(frame), 'd')
        outfr[0] = frame[0] - self.alpha * self.prior
        for i in range(1,len(frame)):
            outfr[i] = frame[i] - self.alpha * frame[i-1]
        self.prior = frame[-1]
        return outfr
        
    def frame2logspec(self, frame):
        frame = self.pre_emphasis(frame) * self.win
        fft = numpy.fft.rfft(frame, self.nfft)
        # Square of absolute value
        power = fft.real * fft.real + fft.imag * fft.imag
        return numpy.log(numpy.dot(power, self.filters).clip(1e-5,numpy.inf))

    def frame2s2mfc(self, frame):
        logspec = self.frame2logspec(frame)
        return numpy.dot(logspec, self.s2dct.T) / self.nfilt

def s2dctmat(nfilt,ncep,freqstep):
    """Return the 'legacy' not-quite-DCT matrix used by Sphinx"""
    melcos = numpy.empty((ncep, nfilt), 'double')
    for i in range(0,ncep):
        freq = numpy.pi * float(i) / nfilt
        melcos[i] = numpy.cos(freq * numpy.arange(0.5, float(nfilt)+0.5, 1.0, 'double'))
    melcos[:,0] = melcos[:,0] * 0.5
    return melcos

def logspec2s2mfc(logspec, ncep=13):
    """Convert log-power-spectrum bins to MFCC using the 'legacy'
    Sphinx transform"""
    nframes, nfilt = logspec.shape
    melcos = s2dctmat(nfilt, ncep, 1./nfilt)
    return numpy.dot(logspec, melcos.T) / nfilt

def dctmat(N,K,freqstep,orthogonalize=True):
    """Return the orthogonal DCT-II/DCT-III matrix of size NxK.
    For computing or inverting MFCCs, N is the number of
    log-power-spectrum bins while K is the number of cepstra."""
    cosmat = numpy.zeros((N, K), 'double')
    for n in range(0,N):
        for k in range(0, K):
            cosmat[n,k] = numpy.cos(freqstep * (n + 0.5) * k)
    if orthogonalize:
        cosmat[:,0] = cosmat[:,0] * 1./numpy.sqrt(2)
    return cosmat

def dct(input, K=13):
    """Convert log-power-spectrum to MFCC using the orthogonal DCT-II"""
    nframes, N = input.shape
    freqstep = numpy.pi / N
    cosmat = dctmat(N,K,freqstep)
    return numpy.dot(input, cosmat) * numpy.sqrt(2.0 / N)

def dct2(input, K=13):
    """Convert log-power-spectrum to MFCC using the normalized DCT-II"""
    nframes, N = input.shape
    freqstep = numpy.pi / N
    cosmat = dctmat(N,K,freqstep,False)
    return numpy.dot(input, cosmat) * (2.0 / N)

def idct(input, K=40):
    """Convert MFCC to log-power-spectrum using the orthogonal DCT-III"""
    nframes, N = input.shape
    freqstep = numpy.pi / K
    cosmat = dctmat(K,N,freqstep).T
    return numpy.dot(input, cosmat) * numpy.sqrt(2.0 / K)

def dct3(input, K=40):
    """Convert MFCC to log-power-spectrum using the unnormalized DCT-III"""
    nframes, N = input.shape
    freqstep = numpy.pi / K
    cosmat = dctmat(K,N,freqstep,False)
    cosmat[:,0] = cosmat[:,0] * 0.5
    return numpy.dot(input, cosmat.T)