clear all
close all
clc
%% Experiment 5.... Auto and Crosscorrelation
x=[1 1 1 1 1 1 1];
y=[6 5 4 3 2 1 0];
N1=length(x);
N2=length(y);
% Built-in function
Rxx_builtin=int32(xcorr(x,x));
Rxy_builtin=int32(xcorr(x,y));
disp('Built-in Rxx:'); disp(Rxx_builtin);
disp('Built-in Rxy:'); disp(Rxy_builtin);
% Manual Calculation
x_rev = fliplr(x);
Lx = N1+N1-1;
Rxx_manual = zeros(1, Lx);
for n = 1:Lx
    for k = 1:N1
        if (n-k+1>0 && n-k+1<=N1)
            Rxx_manual(n)=Rxx_manual(n)+(x(k) * x_rev(n - k + 1));
        end
    end
end
h = fliplr(y);
N = N1+N2-1;
Rxy_manual = zeros(1, N);
for n = 1:N
    for k = 1:N1
        if (n-k+1 > 0 && n-k+1<=N2)
            Rxy_manual(n)=Rxy_manual(n) + (x(k)*h(n-k+1));
        end
    end
end
disp("Manual Rxx:"); disp(Rxx_manual);
disp('Manual Rxy:'); disp(Rxy_manual);
%Plotting
subplot(2,1,1);
stem(Rxx_builtin);
stem(Rxx_manual);
title('Autocorrelation R_{xx}');
xlabel('Sample index');
ylabel('Amplitude');
subplot(2,1,2);
stem(Rxy_builtin);
stem(Rxy_manual);
title('Cross-correlation R_{xy}');
xlabel('Sample index');
ylabel('Amplitude');