DFT Software Implementation

The following functions perform real DFT computation.

MATLAB

function [a, b] = dft(x)
    % Compute the DFT of a real input signal
    N = length(x);         % Number of samples
    n = 0 : N-1;           % Sample indices
    phi = 2 * pi * (n' * n) / N; % Compute angles for DFT matrix

    % Compute cosine and sine frequency components
    a = (2 / N) * cos(phi) * x;
    b = (2 / N) * sin(phi) * x;
end

Python

def dft(x):
    """ Compute DFT of a real input signal """
    N = len(x)
    n = np.arange(N).reshape(1, N) # Create row vector
    phi = 2 * np.pi * n.T * n / N  # Compute angles for DFT matrix

    # Compute cosine and sine frequency components
    a = (2 / N) * np.dot(np.cos(phi), x)
    b = (2 / N) * np.dot(np.sin(phi), x)
    return a, b

C

void dft(double x[], double a[], double b[], int N) {
    // Compute DFT of a real input signal 
    for (int k = 0; k < N; k++) {
        a[k] = 0.0;
        b[k] = 0.0;
        for (int n = 0; n < N; n++) {
            double phi = 2 * PI * k * n / N;
            a[k] += (2.0 / N) * x[n] * cos(phi);
            b[k] += (2.0 / N) * x[n] * sin(phi);
        }
    }
}