%% Exp-9: N-point DFT and FFT

clc; clear; close all;

% Input signal
x = 0:50;             
N = length(x);

% Manual computation of DFT
y = zeros(1, N);
for k = 0:N-1
    for n = 0:N-1
        y(k+1) = y(k+1) + x(n+1) * exp(-1j*2*pi*k*n/N);
    end
end

% FFT computation
X = fft(x);

% Inverse FFT
xx = ifft(X);

% Plot results
figure
subplot(5,1,1)
stem(0:N-1, x); title('Input Signal x(n)');

subplot(5,1,2)
stem(0:N-1, fftshift(abs(y))); title('Magnitude Spectrum (DFT)');

subplot(5,1,3)
stem(0:N-1, angle(y)); title('Phase Spectrum (DFT)');

subplot(5,1,4)
stem(0:N-1, fftshift(abs(X))); title('Magnitude Spectrum (FFT)');

subplot(5,1,5)
stem(0:N-1, real(xx)); title('Reconstructed x(n) using IFFT');