DFT code in matlab with out using FFT function?

Answer 1

To implement the Discrete Fourier Transform (DFT) in MATLAB without using the FFT function, you can use nested loops to compute the DFT directly. The formula for DFT is given by ( X(k) = \sum_{n=0}^{N-1} x(n) e^{-2\pi i nk/N} ), where ( N ) is the length of the input signal ( x ). Here’s a simple implementation:

function X = myDFT(x)
    N = length(x);
    X = zeros(1, N);
    for k = 1:N
        for n = 1:N
            X(k) = X(k) + x(n) * exp(-2 * pi * 1i * (k-1) * (n-1) / N);
        end
    end
end

This code computes the DFT by iterating over each frequency component and summing the contributions from all time-domain samples.