%% Circular Convolution %%

clc;
clear all;
close all;

% Given sequences
x = [1 -1 -2 3 -1];
h = [1 2 3];

n1 = length(x);
n2 = length(h);
N = max(n1, n2);

% Zero-padding
x = [x zeros(1, N - n1)];
h = [h zeros(1, N - n2)];

%% Method-1: Using Circular Convolution Formula
y1 = zeros(1, N);
for n = 0:N-1
    for i = 0:N-1
        j = mod(n - i, N);
        y1(n+1) = y1(n+1) + x(i+1) * h(j+1);
    end
end
disp('Output by Method-1 (Formula):');
disp(y1);

%% Method-2: Using Circulant Matrix
h_temp = h;                % Keep original h for shifting
h_matrix = zeros(N, N);

for n = 1:N
    h_matrix(:, n) = h_temp';
    h_temp = circshift(h_temp, 1);  % Circularly shift right
end

disp('Circulant Matrix:');
disp(h_matrix);

y2 = h_matrix * x';
disp('Output by Method-2 (Matrix):');
disp(y2');

%% Verification
if isequal(round(y1,10), round(y2',10))
    disp('Both methods give the same circular convolution result.');
else
    disp('Mismatch between methods. Check implementation.');
end

%% Plot the sequences
n = 0:N-1;
figure('Name', 'Circular Convolution', 'NumberTitle', 'off');

subplot(3,1,1);
stem(n, x, 'filled');
title('Sequence x(n)');
xlabel('n'); ylabel('Amplitude'); grid on;

subplot(3,1,2);
stem(n, h, 'filled');
title('Sequence h(n)');
xlabel('n'); ylabel('Amplitude'); grid on;

subplot(3,1,3);
stem(n, y1, 'filled');
title('Circular Convolution y(n)');
xlabel('n'); ylabel('Amplitude'); grid on;