dfft ============================================== Purpose ---------------- Computes a discrete Fourier transform. Format ---------------- .. function:: y = dfft(x) :param x: Values used to compute the discrete Fourier transform. :type x: Nx1 vector :return y: The discrete Fourier transform. :rtype y: Nx1 vector Examples ---------------- In this example we will a use a discrete sample of frequencies given by .. math:: f[k] = 5 + 2 * cos(\frac{\pi}{2}k - \frac{\pi}{2}) + 3cos(\pi k) :: // Set k k = seqa(0, 1, 4); // Compute discrete frequencies f_k = 5 + 2 * cos(pi/2*k - 90*pi/180) + 3 * cos(pi*k); After this f_k is equal to: :: 8 4 8 0 Now take the discrete Fourier transform of f_k: :: // Discrete Fourier transform print dfft(f_k); After the code the discrete Fourier transform is printed: :: 5 0 - 1i 3 + 0i 0 + 1i Remarks ------- The transform is divided by :math:N. This uses a second-order Goertzel algorithm. It is considerably slower than :func:fft, but it may have some advantages in some circumstances. For one thing, :math:N does not have to be an even power of 2. Source ------ dfft.src .. seealso:: :func:dffti, :func:fft, :func:ffti