%% Exp-7: Linear Phase FIR Filter
clc; clear; close all;

% Impulse response (symmetric → linear phase FIR)
h = [1 2 3 4 3 2 1];
M = length(h);

% Input signal
x = [0 1 2 3 4 5 6];
Lx = length(x);

% Zero-padding input for full convolution length
x_padded = [x zeros(1, M-1)];
L = length(x_padded);

% Generate shifted versions of x(n)
x_shift = zeros(M, L);
for i = 1:M
    x_shift(i, i:L) = x_padded(1:L - i + 1);
end

% Multiply and sum for manual convolution
for i = 1:M
    y(i, :) = h(i) * x_shift(i, :);
end
op = sum(y);     % Manual convolution output (full length)

% Display results
disp('Input signal x(n):');
disp(x);
disp('Impulse response h(n):');
disp(h);
disp('Shifted versions of x(n):');
disp(x_shift);
disp('Output using manual FIR computation:');
disp(op);

% Built-in convolution
conv1 = conv(x, h);
disp('Output using MATLAB conv():');
disp(conv1);

% Plot comparison
figure;
subplot(2,1,1);
stem(op, 'filled'); title('Output using Manual FIR Computation');
subplot(2,1,2);
stem(conv1, 'filled'); title('Output using Built-in Convolution');