A new efficient algorithm for computing a few DFT points

The authors describe an efficient method for computing the discrete Fourier transform (DFT) when only a few output points are needed. The method is shown to be more efficient than either Goertzel´s method or pruning, and it allows any band in the output to be computed. It is based on a novel factorization of the DFT, where one part is computed using standard power-of-two FFTs (fast Fourier transforms) and the other uses a technique similar to the Goertzel algorithm.<>