% simplistic LPC synthesizer
% must enter pitch and three formant frequencies
% don't expect such a simplistic model to sound natural

function LPCsyn

% let's always use 8000Hz sampling frequency
Fs=8000;

% pitch should be between 100 and 200 Hz
p=200; 

% three formants (Hz)
%f1=650;  f2=850; f3=2500; % AH
%f1=550; f2=1800; f3=2700; % EH
%f1=300; f2=2900; f3=3500; % EE
%f1=450;  f2=800; f3=2800; % O
%f1=370;  f2=950; f3=2650; % OO
%f1=300; f2=2300; f3=3200; % IH
%f1=500;  f2=650; f3=2800; % UH

% convert to digital form
pitch=round(Fs/p);
formant1=f1/Fs;
formant2=f2/Fs;
formant3=f3/Fs;

% place poles according to formant frequencies
p11=0.95*exp(2*pi*i*formant1);
p12=0.95*exp(-2*pi*i*formant1);
p21=0.9*exp(2*pi*i*formant2);
p22=0.9*exp(-2*pi*i*formant2);
p31=0.8*exp(2*pi*i*formant3);
p32=0.8*exp(-2*pi*i*formant3);

% create LPC synthesis filter
[num,den] = zp2tf([],[p11 p12 p21 p22 p31 p32],1);

% create excitation signal ( 1 0 0 0 0 1 0 0 0 0 ...)
excitation=[];
for cnt=[1:200],
    excitation=[excitation 1 zeros(1,pitch-1)];
end

% filter the excitation with the LPC synthesis filter
sig=filter(num,den,excitation);

% remove transient, remove DC and normalize
sig=sig(1000:end);
sig=sig-mean(sig);
sig=sig*(1/max(abs(sig)));

% play it
sound(sig,Fs);