fourier apd

function x = inverseDFT(X)
    % Compute the length of the input DFT
    N = length(X);

    % Compute the IDFT using the formula
    x = zeros(1, N);
    for n = 1:N
        for k = 1:N
            x(n) = x(n) + X(k) * exp(1i * 2 * pi * (k - 1) * (n - 1) / N);
        end
        x(n) = x(n) / N;
    end
end
% Generate a random input signal
signal = rand(1, 8);

% Compute the DFT of the input signal
X = fft(signal);

% Compute the IDFT of the DFT result
reconstructed_signal = inverseDFT(X);

% Check if the input signal and the reconstructed signal are the same
disp('Original Signal:');
disp(signal);
disp('Reconstructed Signal:');
disp(real(reconstructed_signal));

% Compare the original signal and the reconstructed signal
if isequal(signal, real(reconstructed_signal))
    disp('DFT and IDFT are inverses of each other.');
else
    disp('DFT and IDFT are NOT inverses of each other.');
end