%=============================8.3.2 Plain LPC Decoder================================%

function synWave = synlpc(aCoeff,pitch,sr,G,fr,fs,preemp)
% USAGE: synWave = synlpc(aCoeff,pitch,sr,G,fr,fs,preemp);
%
% This function synthesizes a (speech) signal based on a LPC (linear-
% predictive coding) model of the signal. The LPC coefficients are a 
% short-time measure of the speech signal which describe the signal as the 
% output of an all-pole filter. This all-pole filter provides a good 
% description of the speech articulators; thus LPC analysis is often used in 
% speech recognition and speech coding systems. The LPC analysis is done
% using the proclpc routine. This routine can be used to verify that the 
% LPC analysis produces the correct answer, or as a synthesis stage after
% first modifying the LPC model.
%
% The results of LPC analysis are a new representation of the signal
% s(n) = G e(n) - sum from 1 to L a(i)s(n-i)
% where s(n) is the original data. a(i) and e(n) are the outputs of the LPC 
% analysis with a(i) representing the LPC model. The e(n) term represents 
% either the speech source's excitation, or the residual: the details of the 
% signal that are not captured by the LPC coefficients. The G factor is a
% gain term.
%
% LPC synthesis produces a monaural sound vector (synWave) which is 
% sampled at a sampling rate of "sr". The following parameters are mandatory
% aCoeff - The LPC analysis results, a(i). One column of L+1 numbers for each
% frame of data. The number of rows of aCoeff determines L.
% G - The LPC gain for each frame.
% pitch - A frame-by-frame estimate of the pitch of the signal, calculated
% by finding the peak in the residual's autocorrelation for each frame.
%
% The following parameters are optional and default to the indicated values.
% fr - Frame time increment, in ms. The LPC analysis is done starting every
% fr ms in time. Defaults to 20ms (50 LPC vectors a second)
% fs - Frame size in ms. The LPC analysis is done by windowing the speech
% data with a rectangular window that is fs ms long. Defaults to 30ms
% preemp - This variable is the epsilon in a digital one-zero filter which 
% serves to preemphasize the speech signal and compensate for the 6dB
% per octave rolloff in the radiation function. Defaults to .9378.

if (nargin < 5), fr = 20; end;
if (nargin < 6), fs = 30; end;
if (nargin < 7), preemp = .9378; end;

msfs = round(sr*fs/1000); % framesize in samples
msfr = round(sr*fr/1000); % framerate in samples
msoverlap = msfs - msfr;
ramp = [0:1/(msoverlap-1):1]';
[L1 nframe] = size(aCoeff); % L1 = 1+number of LPC coeffs 

for frameIndex=1:nframe
A = aCoeff(:,frameIndex);
% first check if it is voiced or unvoiced sound:
if ( pitch(frameIndex) ~= 0 )
t = 0 : 1/sr : fs*10^(-3); % sr sample freq. for fr ms
d = 0 : 1/pitch(frameIndex) : 1; % 1/pitchfreq. repetition freq.
residFrame = (pulstran(t, d, 'tripuls', 0.001))'; % sawtooth width of 0.001s
residFrame = residFrame + 0.01*randn(msfs+1,1);
else
residFrame = [];
for m = 1:msfs
residFrame = [residFrame; randn];
end % for
end;

synFrame = filter(G(frameIndex), A', residFrame); % synthesize speech from LPC coeffs
if(frameIndex==1) % add synthesize frames using a trapezoidal window
synWave = synFrame(1:msfr);
else
synWave = [synWave; overlap+synFrame(1:msoverlap).*ramp; ...
synFrame(msoverlap+1:msfr)];
end
if(frameIndex==nframe)
synWave = [synWave; synFrame(msfr+1:msfs)];
else
overlap = synFrame(msfr+1:msfs).*flipud(ramp); 
end 
end;

synWave = filter(1, [1 -preemp], synWave);