wolffd@0: function [output,aCoeff] = WhiteVowel(data,sr,L,pos)
wolffd@0: % function [output,aCoeff] = WhiteVowel(data,sr,L,pos)
wolffd@0: %
wolffd@0: % Speech is often described as having spectral peaks or formants which 
wolffd@0: % identify the phonetic signal. An interesting experiment, first proposed by
wolffd@0: % XXX, filters a speech signal to remove all the formant information at one
wolffd@0: % time during the speech. If there are no formant peaks, how can the speech
wolffd@0: % be understood?  It turns out that processing, much like RASTA, means that
wolffd@0: % relative changes in spectrum are the most important, thus the speech signal
wolffd@0: % is understood because the formant transitions carry the information.  This
wolffd@0: % gives speech an important transparency due 
wolffd@0: %
wolffd@0: % This function takes a speech signal (data) with a given sampling rate (sr).
wolffd@0: % It then finds the L-order LPC filter that describes the speech at the given
wolffd@0: % position (pos ms).  The entire speech signal is then filtered with the
wolffd@0: % inverse of the LPC filter, effectively turning the speech spectrum at the 
wolffd@0: % given time white (flat).
wolffd@0: 
wolffd@0: % Chris Pal, Interval, May 1997
wolffd@0: % (c) 1998 Interval Research Corporation  
wolffd@0: 
wolffd@0: fr = 20; fs = 30; preemp = .9378;			% LPC defaults
wolffd@0: 
wolffd@0: [row col] = size(data);
wolffd@0: if col==1 data=data'; end
wolffd@0: 
wolffd@0: nframe = 0;
wolffd@0: msfr = round(sr/1000*fr);
wolffd@0: msfs = round(sr/1000*fs);
wolffd@0: duration = length(data);
wolffd@0: msoverlap = msfs - msfr;
wolffd@0: frameNumber = floor(pos/1000*sr/msfr);
wolffd@0: 
wolffd@0: frameStart = round(pos/1000*sr - msfs/2);	                
wolffd@0: frameData = data(frameStart:(frameStart+msfs-1));   
wolffd@0: aCoeff = proclpc(frameData, sr, L, fr, fs, preemp);
wolffd@0:                                 % Calculate the filter response
wolffd@0:                                 % by evaluating the z-transform
wolffd@0: spec=lpc_spec(aCoeff);
wolffd@0: subplot(2,3,1);
wolffd@0: plot(spec);
wolffd@0: title('LPC Spectral Slice');
wolffd@0: ylabel('Original')
wolffd@0: 
wolffd@0: 								% Now do the actual whitening filter
wolffd@0: output = filter(aCoeff,1,data)';
wolffd@0: 
wolffd@0: frameData = output(frameStart:(frameStart+msfs-1));   
wolffd@0: bCoeff = proclpc(frameData, sr, L, fr, fs,  preemp);
wolffd@0: spec=lpc_spec(bCoeff);
wolffd@0: subplot(2,3,4);
wolffd@0: plot(spec);
wolffd@0: ylabel('Whitened'); xlabel('FFT Bin');
wolffd@0: 
wolffd@0: % 256-DFT
wolffd@0: origSpec = 20*log10(abs(specgram(data,512,sr,msfs,msoverlap)));
wolffd@0: subplot(2,3,2),imagesc(origSpec); axis xy; colormap(1-gray);
wolffd@0: title('Spectrogram');
wolffd@0: 
wolffd@0: synSpec = 20*log10(abs(specgram(output,512,sr,msfs,msoverlap)));
wolffd@0: subplot(2,3,5),imagesc(synSpec); axis xy; colormap(1-gray);
wolffd@0: xlabel('Frame #');
wolffd@0: 
wolffd@0: origloc = origSpec(:,frameNumber); origloc=origloc-max(origloc);origmin=min(origloc);
wolffd@0: subplot(2,3,3),plot(origloc),title('Spectrogram'),
wolffd@0: axis([1 length(origloc) origmin 0]);
wolffd@0: 
wolffd@0: filloc = synSpec(:,frameNumber); filloc=filloc-max(filloc);
wolffd@0: subplot(2,3,6),plot(filloc);ylabel('db');
wolffd@0: axis([1 length(origloc) origmin 0]);
wolffd@0: xlabel('FFT Bin');
wolffd@0: 
wolffd@0: function spec=lpc_spec(aCoeff)
wolffd@0: gain=0;
wolffd@0: cft=0:(1/255):1;
wolffd@0: for index=1:size(aCoeff,1)
wolffd@0:  gain = gain + aCoeff(index)*exp(-i*2*pi*cft).^index;
wolffd@0: end
wolffd@0: gain = abs(1./gain);
wolffd@0: spec = 20*log10(gain(1:128))';