Efficient FFT algorithm based on the DST

Abstract

It is shown that the N-point DFT (discrete Fourier transform) of a real sequence can be implemented via the real (cos DFT) and imaginary (sin DFT) components. The N-point cos DFT in turn can be developed from the N/2-point cos DFT and N/4-point discrete sine transform (DST). Similarly the N-point sin DFT can be developed from N/2-point sin DFT and N-point DST. Using this approach, an efficient algorithm (involving real arithmetic only) for an N-point DFT is developed. The basic DST algorithm has an orderly architecture and recursive structure. Because of its regularity and symmetry, the algorithm is conducive to simple hardware implementation. >