632 lab 4 AB

%% Part A
%problem 1
xn=[1 6/7 5/7 4/7 3/7 2/7 1/7 zeros(1,121)];
n=0:127;
xf=fft(xn);
xf=fftshift(xf);
plot(n.*2*pi/128,abs(xf));
title("fft calculated magnitude plot");
figure;
plot(n.*2*pi/128,angle(xf));
title("fft calculated phase plot");

%problem 2
%{
xf2=zeros(1,128);
omega=linspace(-pi,pi,128);
temp=1;
for omega= linspace(-pi,pi,128)
    xf2(temp)=sum(xn.*exp(-1i*omega*n));
    temp=temp+1;
end
%}
xomega=@(o) exp(-0i.*o) + (6/7)*exp(-i.*o) + (5/7)*exp(-2i.*o) + (4/7)*exp(-3i.*o) + (3/7)*exp(-4i.*o) + (2/7)*exp(-5i.*o) + (1/7)*exp(-6i.*o);
figure;
omega=n.*2*pi/128;
xf2=xomega(omega);
xf2=fftshift(xf2);
plot(omega,abs(xf2));
title("Manually calculated magnitude plot");
figure;
plot(omega,angle(xf2));
title("Manually calculated phase plot");

%Problem 3
Xn=ifft(xf);
figure;
stem(n,Xn);
title("original signal without abs function");
figure;
stem(n,abs(Xn));
title("original signal with abs function");

%% Part B

un= @(n) 1.0.*(n>=0);
und= @(n) un(n).*(mod(n,1)==0);
n=[0:15];
xn=sin(2*pi.*n/10).*(und(n)-und(n-10));
omega=linspace(-pi,pi,1001);
W_omega1=exp(-j).^((0:length(xn)-1)'*omega);
X1=(xn*W_omega1);
plot(omega, abs(X1));
title("magnitude of x[n] FT");
figure;
plot(omega, angle(X1));
title("phase of x[n] FT");
figure;
hn=und(n)-und(n-10);
W_omega2=exp(-j).^((0:length(hn)-1)'*omega);
X2=(hn*W_omega2);
plot(omega, abs(X2));
title("magnitude of h[n] FT");
figure;
plot(omega, angle(X2));
title("phase of h[n] FT");
figure;
yf=X1.*X2;
plot(omega,abs(yf));
title("magnitude of X[\Omega]H[\Omega]");
figure;
plot(omega, angle(yf));
title("phase of X[\Omega]H[\Omega]");
yn=conv(xn,hn);
W_omega3=exp(-j).^((0:length(yn)-1)'*omega);
X3=(yn*W_omega3);
figure;
plot(omega,abs(X3));
title("magnitude of y[n]");
figure;
plot(omega,angle(X3));
title("phase of y[n]");

disp("convolution in the time domain is the same thing as multiplication in the frequency domain");