Efficient matched filters for DFT based codes

A computationally efficient matched filter for Frank polyphase and similar Discrete Fourier Transform (DFT) related codes is proposed. It is based on converting any available efficient Short Time Fourier Transform (STFT) algorithm into a related matched filter. This results in significant computational advantage over the existing methods. In comparison to the Goertzel algorithm, it offers guaranteed stability and reduced roundoff noise, in addition to reducing the required computation by half. The best known non-recursive methods, in which an FFT is applied for each new input, require O(N log N) multiplications per output instead of the O(N) for the proposed STFT based matched filters.