wolffd@0: function synWave = synlpc(aCoeff,source,sr,G,fr,fs,preemp)
wolffd@0: % USAGE: synWave = synlpc(aCoeff,source,sr,G,fr,fs,preemp);
wolffd@0: %
wolffd@0: % This function synthesizes a (speech) signal based on a LPC (linear-
wolffd@0: % predictive coding) model of the signal.  The LPC coefficients are a 
wolffd@0: % short-time measure of the speech signal which describe the signal as the 
wolffd@0: % output of an all-pole filter.  This all-pole filter provides a good 
wolffd@0: % description of the speech articulators; thus LPC analysis is often used in 
wolffd@0: % speech recognition and speech coding systems.  The LPC analysis is done
wolffd@0: % using the proclpc routine.  This routine can be used to verify that the 
wolffd@0: % LPC analysis produces the correct answer, or as a synthesis stage after
wolffd@0: % first modifying the LPC model.
wolffd@0: %
wolffd@0: % The results of LPC analysis are a new representation of the signal
wolffd@0: %	s(n) = G e(n) - sum from 1 to L a(i)s(n-i)
wolffd@0: % where s(n) is the original data.  a(i) and e(n) are the outputs of the LPC 
wolffd@0: % analysis with a(i) representing the LPC model. The e(n) term represents 
wolffd@0: % either the speech source's excitation, or the residual: the details of the 
wolffd@0: % signal that are not captured by the LPC coefficients.  The G factor is a
wolffd@0: % gain term.
wolffd@0: %
wolffd@0: % LPC synthesis produces a monaural sound vector (synWave) which is 
wolffd@0: % sampled at a sampling rate of "sr".  The following parameters are mandatory
wolffd@0: % aCoeff - The LPC analysis results, a(i).  One column of L+1 numbers for each
wolffd@0: %	frame of data.  The number of rows of aCoeff determines L.
wolffd@0: % source - The LPC residual, e(n).  One column of sr*fs samples representing
wolffd@0: %	the excitation or residual of the LPC filter.
wolffd@0: % G - The LPC gain for each frame.
wolffd@0: %
wolffd@0: % The following parameters are optional and default to the indicated values.
wolffd@0: % fr - Frame time increment, in ms.  The LPC analysis is done starting every
wolffd@0: % 	fr ms in time.  Defaults to 20ms (50 LPC vectors a second)
wolffd@0: % fs - Frame size in ms.  The LPC analysis is done by windowing the speech
wolffd@0: % 	data with a rectangular window that is fs ms long.  Defaults to 30ms
wolffd@0: % preemp - This variable is the epsilon in a digital one-zero filter which 
wolffd@0: %	serves to preemphasize the speech signal and compensate for the 6dB
wolffd@0: %	per octave rolloff in the radiation function.  Defaults to .9378.
wolffd@0: %
wolffd@0: % This code was graciously provided by:
wolffd@0: % 	Delores Etter (University of Colorado, Boulder) and 
wolffd@0: %	Professor Geoffrey Orsak (Southern Methodist University) 
wolffd@0: % It was first published in
wolffd@0: %	Orsak, G.C. et al. "Collaborative SP education using the Internet and
wolffd@0: %	MATLAB" IEEE SIGNAL PROCESSING MAGAZINE  Nov. 1995. vol.12, no.6, pp.
wolffd@0: %	23-32.
wolffd@0: % Modified and debugging plots added by Kate Nguyen and Malcolm Slaney
wolffd@0: 
wolffd@0: % (c) 1998 Interval Research Corporation  
wolffd@0: % A more complete set of routines for LPC analysis can be found at
wolffd@0: %	http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
wolffd@0:    
wolffd@0: 
wolffd@0: 
wolffd@0: if (nargin < 5), fr = 20; end;
wolffd@0: if (nargin < 6), fs = 30; end;
wolffd@0: if (nargin < 7), preemp = .9378; end;
wolffd@0: 
wolffd@0: msfs = round(sr*fs/1000);
wolffd@0: msfr = round(sr*fr/1000);
wolffd@0: msoverlap = msfs - msfr;
wolffd@0: ramp = [0:1/(msoverlap-1):1]';
wolffd@0: [L1 nframe] = size(aCoeff); 			% L1 = 1+number of LPC coeffs 
wolffd@0: 
wolffd@0: [row col] = size(source);
wolffd@0: if(row==1 | col==1)				% continous stream; must be 
wolffd@0: 						% windowed
wolffd@0:   postFilter = 0; duration = length(source); frameIndex = 1;
wolffd@0:   for sampleIndex=1:msfr:duration-msfs+1
wolffd@0:     resid(:,frameIndex) = source(sampleIndex:(sampleIndex+msfs-1))';
wolffd@0:     frameIndex = frameIndex+1;    
wolffd@0:   end
wolffd@0: else
wolffd@0:   postFilter = 1; resid = source;
wolffd@0: end
wolffd@0: 
wolffd@0: [row col] = size(resid);
wolffd@0: %if ~(col==nframe)
wolffd@0: %  error('synLPC: numbers of LPC frames and source frames do not match');
wolffd@0: if col<nframe  
wolffd@0:   nframe=col;
wolffd@0: end
wolffd@0: 
wolffd@0: for frameIndex=1:nframe
wolffd@0:  						% Calculate the filter response
wolffd@0: 						% by evaluating the z-transform
wolffd@0: %  if 1
wolffd@0: %    gain=0;
wolffd@0: %    cft=0:(1/255):1;
wolffd@0: %    for index=1:L1-1
wolffd@0: %      gain = gain + aCoeff(index,frameIndex)*exp(-i*2*pi*cft).^index;
wolffd@0: %    end
wolffd@0: %    gain = abs(1./gain);
wolffd@0: %    spec(:,frameIndex) = 20*log10(gain(1:128))';
wolffd@0:     % plot(20*log10(gain));
wolffd@0:     % title(frameIndex);
wolffd@0:     % drawnow;
wolffd@0: %  end
wolffd@0: 
wolffd@0: 						% Calculate the filter response
wolffd@0: 						% from the filter's impulse
wolffd@0: 						% response (to check above).
wolffd@0: %  if 0
wolffd@0: %    impulseResponse = filter(1, aCoeff(:,frameIndex), [1 zeros(1,255)]);
wolffd@0: %    freqResp = 20*log10(abs(fft(impulseResponse)));
wolffd@0: %    plot(freqResp);
wolffd@0: %  end
wolffd@0: 
wolffd@0: 
wolffd@0:   A = aCoeff(:,frameIndex);
wolffd@0:   residFrame = resid(:,frameIndex)*G(frameIndex);
wolffd@0:   synFrame = filter(1, A', residFrame);		% synthesize speech from LPC 
wolffd@0: 						% coeffs
wolffd@0:   if(frameIndex==1)				% add synthesize frames using a
wolffd@0:     synWave = synFrame(1:msfr);			% trapezoidal window
wolffd@0:   else
wolffd@0:     synWave = [synWave; overlap+synFrame(1:msoverlap).*ramp; ...
wolffd@0: 			synFrame(msoverlap+1:msfr)];
wolffd@0:   end
wolffd@0:   if(frameIndex==nframe)
wolffd@0:     synWave = [synWave; synFrame(msfr+1:msfs)];
wolffd@0:   else
wolffd@0:     overlap = synFrame(msfr+1:msfs).*flipud(ramp);	
wolffd@0:   end	
wolffd@0:   %length(synWave)						
wolffd@0: end;
wolffd@0: 
wolffd@0: if(postFilter)
wolffd@0:   synWave = filter(1, [1 -preemp], synWave);
wolffd@0: end
wolffd@0: