%Matlab file used for class demo conducted during Session 23
%illustrating efficacy of M-Channel PR Filter Bank
%when arbitrary FIR analysis filters of length M are used
%Three examples are illustrated:  M pt DFT matrix,
%MxM Hadamard matrix, and even a case where the filters
%are random Gaussian vectors of length M
clf
clear all
set(0,'defaultaxesfontsize',20);
%Set up M-channel DFT filter bank:
M=8;
%H=dftmtx(M);
%H=hadamard(M);
H=randn(M,M);
Gt=inv(H).';  G=Gt(:,M:-1:1);
%
data=getspeech('00f1s2t0.wav');
Fs=12500;
clf
plot(data)
end1=input('end1?');
end2=input('end2?');
xr=data(end1:end2);
dl=end2-end1+1;
%change sampling rate to 10 KHz
x=resample(xr,4,5);
Fs=(4/5)*Fs;
input('Utterance played back at 10 KHz sampling rate'); 
soundsc(x,Fs)
%create x_0 [n] through x_M-1 [n]
for m=1:M;
W(m,:)=conv(x,H(m,:));
X(m,:)=W(m,1:M:length(W(m,:)));
end
%create y_0[n] and y_M-1 [n]
for m=1:M;
Z(m,:)=zeros(1,M*length(X(m,:)));
Z(m,1:M:length(Z(m,:)))=X(m,:);
Y(m,:)=conv(Z(m,:),G(m,:));
end
y=zeros(1,length(Y(1,:)));
for m=1:M;
y=y+Y(m,:);
end
y=real(y);
input('QMF Output played back at Fs=10 KHz'); 
soundsc(y,Fs)
%plot and compare DTFT's of x[n] and y[n]
domega=2*pi/8192;
omega=-pi:domega:pi-domega;
yf1=abs(fftshift(fft(x,8192)));
yf2=abs(fftshift(fft(y,8192)));
subplot(211)
plot(omega,yf1,'Linewidth',3)
axis([-pi pi 0 max(yf1)])
title('DTFT of original utterance');
xlabel('omega (radians/s)');
subplot(212)
plot(omega,yf2,'Linewidth',3)
axis([-pi pi 0 max(yf2)])
title('DTFT of output of QMF');
xlabel('omega (radians/s)');
%plot filter responses h[n]
h0=H(1,:);  h1=H(2,:);
hlf=abs(fftshift(fft(h0,512)));
hpf=abs(fftshift(fft(h1,512)));
input('Plot DTFT of h0[n] and h1[n]')
clf
domega=2*pi/512;
omega=-pi:domega:pi-domega;
plot(omega,hlf,'b','Linewidth',4)
axis([-pi pi 0 max(hlf)])
hold on
plot(omega,hpf,'r','Linewidth',4)
legend('H0(w)','H1(w)');
title('Frequency Response of h0[n] and h1[n]');
xlabel('omega (radians/s)');
hold off
pause
%plot and compare DTFT's of x0[n] and x1[n]
x0=X(1,:);  x1=X(2,:);
domega=2*pi/4096;
omega=-pi:domega:pi-domega;
xf1=abs(fftshift(fft(x0,4096)));
xf2=abs(fftshift(fft(x1,4096)));
subplot(211)
plot(omega,xf1,'Linewidth',3)
axis([-pi pi 0 max(xf1)])
title('DTFT of x0[n]');
xlabel('omega (radians/s)');
subplot(212)
plot(omega,xf2,'Linewidth',3)
axis([-pi pi 0 max(xf2)])
title('DTFT of x1[n]');
xlabel('omega (radians/s)');