clear all
close all
clc
%% Experiment 4.... Linear Convolution
x=[1 2 1 2]; nx1=-1;
h=[2 1 2 3]; nh1=0;
y1=conv(x,h);
N1=length(x);
N2=length(h);
N=N1+N2-1;
y_manual_1=zeros(1,N);
for n=1:N
    for k=1:N1
        if(n-k+1>0 && n-k+1<=N2)
            y_manual_1(n)=y_manual_1(n)+(x(k)*h(n-k+1));
        end
    end
end
ny1 = nx1 + nh1;                   % starting index of y
ny2 = ny1 + (N-1);                 % ending index of y
ny  = ny1:ny2;
y_manual_2=zeros(1,N1+N2-1);
for i=1:length(x)
    for j=1:length(h)
        y_manual_2(i+j-1)=y_manual_2(i+j-1)+(x(i)*h(j));
    end
end
% Display result
disp("Input Sequence x(n)"); disp(x)
disp("Impulse Sequence h(n)"); disp(h)
disp("Convolution result using built-in function:"); disp(y1)
disp("Convolution result manually (with index shift):"); disp(y_manual_2)
disp("Output index range n="+string(ny1)+" to "+string(ny2))
% Plotting
subplot(2,2,1);
stem(nx1:nx1+N1-1,x,"filled");
title("Input Sequence x(n)"); xlabel("n"); ylabel("x(n)")
subplot(2,2,2);
stem(nh1:nh1+N2-1,h,"filled");
title("Impulse Response h(n)"); xlabel("n"); ylabel("h(n)")
subplot(2,2,3);
stem(ny,y_manual_2,"filled");
title("Manual Convolution y(n)"); xlabel("n"); ylabel("y(n)")
subplot(2,2,4);
stem(ny,y1,"filled");
title("Built-in Convolution y(n)"); xlabel("n"); ylabel("y(n)")