mfcc.m

function [ MFCC, FBE, frames ] = mfcc( speech, fs, Tw, Ts, alpha, window, R, M, N, L )
% MFCC Mel frequency cepstral coefficient feature extraction.
%   Inputs
%           S is the input speech signal (as vector)
%
%           FS is the sampling frequency (Hz) 
%
%           TW is the analysis frame duration (ms) 
% 
%           TS is the analysis frame shift (ms)
%
%           ALPHA is the preemphasis coefficient
%
%           WINDOW is a analysis window function handle
% 
%           R is the frequency range (Hz) for filterbank analysis
%
%           M is the number of filterbank channels
%
%           N is the number of cepstral coefficients 
%             (including the 0th coefficient)
%
%           L is the liftering parameter
%
%   Outputs
%           MFCC is a matrix of mel frequency cepstral coefficients
%              (MFCCs) with feature vectors as columns
%
%           FBE is a matrix of filterbank energies
%               with feature vectors as columns
%
%           FRAMES is a matrix of windowed frames
%                  (one frame per column)


    % Ensure correct number of inputs
    if( nargin~= 10 ), help mfcc; return; end; 

    % Explode samples to the range of 16 bit shorts
    if( max(abs(speech))<=1 ), speech = speech * 2^15; end;

    Nw = round( 1E-3*Tw*fs );    % frame duration (samples)
    Ns = round( 1E-3*Ts*fs );    % frame shift (samples)

    nfft = 2^nextpow2( Nw );     % length of FFT analysis 
    K = nfft/2+1;                % length of the unique part of the FFT 


    %% HANDY INLINE FUNCTION HANDLES

    hz2mel = @( hz )( 1127*log(1+hz/700) );     % Hertz to mel warping function
    mel2hz = @( mel )( 700*exp(mel/1127)-700 ); % mel to Hertz warping function

    % Type III DCT matrix routine (DCT - Discrete Cosine Transform)
    dctm = @( N, M )( sqrt(2.0/M) * cos( repmat([0:N-1].',1,M) ...
                                       .* repmat(pi*([1:M]-0.5)/M,N,1) ) );

    % Cepstral lifter routine 
    ceplifter = @( N, L )( 1+0.5*L*sin(pi*[0:N-1]/L) );


    %% FEATURE EXTRACTION 

    speech = filter( [1 -alpha], 1, speech ); % fvtool( [1 -alpha], 1 ); First order FIR Filter

    % Framing and windowing (frames as columns)
    frames = vec2frames( speech, Nw, Ns, 'cols', window, false );

    % Magnitude spectrum computation (as column vectors)
    MAG = abs( fft(frames,nfft,1) ); 

    % Triangular filterbank with uniformly spaced filters on mel scale
    H = trifbank( M, K, R, fs, hz2mel, mel2hz ); % size of H is M x K 

    % Filterbank application to unique part of the magnitude spectrum
    FBE = H * MAG(1:K,:); % FBE( FBE<1.0 ) = 1.0; % apply mel floor

    % DCT matrix computation
    DCT = dctm( N, M );

    % Conversion of logFBEs to cepstral coefficients through DCT
    MFCC =  DCT * log( FBE );

    % Cepstral lifter computation
    lifter = ceplifter( N, L );
     
    % Cepstral liftering gives liftered cepstral coefficients
    MFCC = diag( lifter ) * MFCC; % ~ HTK's MFCCs


% EOF