%--------------------------------------------------------------------------
%Jeniffer Estrada
%All rights reserved.
%This is for educational purposes only.
%November 8, 2008
%--------------------------------------------------------------------------
%Problem 1: Time Domain convolution using two user input functions.

%Part A: Sample h(t) and x(t) over the interval (0,T) using N samples. 
%Gives the sampled values h(n) and x(n) in a discrete plot or list.
%Give the values of time corresponding to n.

T=input('Enter Interval: 0-');
t=0:0.1:T; %60 samples
x=input('Enter first function to be convolved:');
h=('Enter second function to be convolved:');
a =conv(h,x);
n= 0:length(a)-1;
t1=t';
x_sampled=exp(-n); %values of h(n)
h_sampled=2*exp(-n); %values of h(n)
samples=[x_sampled; h_sampled]'; %List of h(n) and x(n)
conversion=[t n]; % The value of time corresponding to n

%%--------------------------------------------------------------------------
%Part B: Gives the sample values y(n)=h(n)*x(n) in a discrete plot.
y=conv(h,x);
figure
plot(n,y,'.');
title('Discrete Representation of Convolution with n samples')
xlabel('n');
ylabel('y(n)');

%--------------------------------------------------------------------------
%Part C: Give a plot of y(t). Label the axies properly.
figure
plot(t,y(1:61),'.');
title('Discrete Representation of Convolution with t samples')
xlabel('t');
ylabel('y(t)');

%--------------------------------------------------------------------------

%Problem 2: Using the Discrete Fourier Transform for convolution:

%Part A: Gives both the magnitude and phase of the DFT's H(k) and X(k).
%Gives a list or discrete plot. Gives the value of w corresponding to k.
X=fft(x); %Conversion from time domain to Fourier Domain.
X_Magnitude=abs(X);
X_Phase=angle(X);
k_limit=length(X);
k=1:k_limit;
figure
plot(k,X_Magnitude,'.');
title('Discrete Representation of X Magnitude in Fourier Domain')
xlabel('k');
ylabel('Magnitude');

figure
plot(k,X_Phase,'.');
title('Discrete Representation of X Phase in Fourier Domain')
xlabel('k');
ylabel('Phase');



H=fft(h); %Conversion to Fourier Domain.
H_Magnitude=abs(H);
H_Phase=angle(H);
figure
plot(k,H_Magnitude,'.');
title('Discrete Representation of H Magnitude in Fourier Domain')
xlabel('k');
ylabel('Magnitude');

figure
plot(k,H_Phase,'.');
title('Discrete Representation of H Phase in Fourier Domain')
xlabel('k');
ylabel('Phase');

%--------------------------------------------------------------------------
%Part B: Give the magitude and phase of the DFT's Y(k)=H(k)*X(k).
Y=H.*X;
magnitude=abs(Y);
phase=angle(Y);

%Discrete plot of Magnitude and Phase of Y with respect to k.
figure
plot(k,magnitude, '.');
title('Discrete Representation of Y Magnitude in Fourier Domain')
xlabel('k');
ylabel('Magnitude');

%Continous plot of Magnitude and Phase of Y with respect to k.
figure
plot(k,magnitude);
title('Continuous Representation of Y Magnitude in Fourier Domain')
xlabel('k');
ylabel('Magnitude');

%Discrete plot of Magnitude and Phase of Y with respect to k.
figure
plot(k,phase,'.');
title('Discrete Representation of Y Phase in Fourier Domain')
xlabel('k');
ylabel('Phase');

%Continous plot of Magnitude and Phase of Y with respect to k.
figure
plot(k,phase);
title('Continuous Representation of Y Phase in Fourier Domain')
xlabel('k');
ylabel('Phase');