%Matlab file used for class demo conducted during clas
%illustrating upsampling by a factor of 3 using the
%efficient polyphase implementation of upsampling.
%A word utterance is sampled at 12.5 KHz, upsampled by
%a factor of 3 and played back at 37.5 KHz
clf
clear all
set(0,'defaultaxesfontsize',20);
wc=9*pi/10;
end1=100;
n=-end1:end1; 
beta=0.1;
n0=n+0.000001;
h0=sin(pi*n0)./(pi*n0);
%h0=(sin(wc*n0)./(wc*n0)).*(cos(beta*wc*n0)./(1-(4/pi^2)*beta^2*(wc*n0).^2));
n1=n+(1/3);
h1=sin(pi*n1)./(pi*n1);
%h1=(sin(wc*n1)./(wc*n1)).*(cos(beta*wc*n1)./(1-(4/pi^2)*beta^2*(wc*n1).^2));
n2=n+(2/3);
h2=sin(pi*n2)./(pi*n2);
%h2=(sin(wc*n2)./(wc*n2)).*(cos(beta*wc*n2)./(1-(4/pi^2)*beta^2*(wc*n2).^2));
x=getspeech('0wf1s1t0.wav');
x=x(500:13500);  ll=13500-500+1;
Fs=12500;
input('Utterance played back at orignal sampling rate, Fs = 12.5 KHz'); 
soundsc(x,Fs)
y1=conv(x,h0); 
y2=conv(x,h1); y3=conv(x,h2);
%y1=zeros(size(y2)); y1(1,102:102+ll-1)=x;
l3=3*length(y1);
y=zeros(1,l3);
y(1:3:l3)=y1; y(2:3:l3)=y2; y(3:3:l3)=y3;
input('Utterance interpolated by a factor played at thrice sampling rate, 3*Fs = 37.5 KHz');
soundsc(y,3*Fs)
%
N1=16384;
N2=65536;
omega1=linspace(-pi,pi,N1);
omega2=linspace(-pi,pi,N2);
yf1=abs(fftshift(fft(x,N1)));
yf2=abs(fftshift(fft(y(75:end-75),N2)));
subplot(211)
plot(omega1,yf1,'Linewidth',3)
axis([-pi pi 0 max(yf1)])
title('DTFT of original utterance');
%xlabel('omega (radians/s)');
subplot(212)
plot(omega2,yf2,'Linewidth',3)
axis([-pi pi 0 max(yf2)])
title('DTFT of utterance interpolated by a factor of 3');
xlabel('omega (radians/s)');
pause
domega=2*pi/1024;
omega=-pi:domega:pi-domega;
hf0=abs(fftshift(fft(h0,1024)));
hf1=abs(fftshift(fft(h1,1024)));
hf2=abs(fftshift(fft(h2,1024)));
subplot(211)
plot(omega,hf1,'Linewidth',3)
axis([-pi pi 0 max(hf1)])
title('DTFT of Filter 1');
%xlabel('omega (radians/s)');
subplot(212)
plot(omega,hf2,'Linewidth',3)
axis([-pi pi 0 max(hf2)])
title('DTFT of Filter 2');
xlabel('omega (radians/s)');
pause
domega=2*pi/1024;
omega=-pi:domega:pi-domega;
hfa0=angle(exp(j*end1*omega).*fftshift(fft(h0,1024)));
hfa1=angle(exp(j*end1*omega).*fftshift(fft(h1,1024)));
hfa2=angle(exp(j*end1*omega).*fftshift(fft(h2,1024)));
subplot(211)
plot(omega,hfa0,'Linewidth',3)
axis([-pi pi -pi pi])
hold on 
plot(omega,hfa1,'-r','Linewidth',3)
plot(omega,hfa2,'-k','Linewidth',3)
legend('Phase of H0(w): slope=0','Phase of H1(w): slope=1/3','Phase of H2(w): slope=2/3')
hold off
title('Phase of 3 Polyphase Filters');
%xlabel('omega (radians/s)');
subplot(212)
plot(omega,hf0,'-b','Linewidth',3)
axis([-pi pi 0 max(hf0)])
title('Magnitude of Filter 0');
xlabel('omega (radians/s)');
SlopeH1=mean(diff(hfa1(24:end-24)))/domega
SlopeH2=mean(diff(hfa2(24:end-24)))/domega
