General - N Winograd D.F.T. programs with inverse option

Abstract

S. Winograd's papers "On computing the discrete Fourier transform" (1976 and 1978) allow one to know the minimum number of multiplications to compute a DFT if the length is a power of a prime and to build such algorithms for small lengths. It is suggested that longer transforms be 'built up' with the short algorithms. For this Winograd proposes and Kolba & Parks detail two ways I.J Good's prime factor algorithm and Winograd's modified by J.H McClellan nested prime factor algorithm. In 1979 J.H McClellan publishes a General-N FORTRAN program (WFTA) using the nested algorithm. In 1981 C.S Burrus publishes a very simple program (PFA1) using in place the prime factor algorithm. In 1982 J.H Rothweller extends an idea of Burrus to developp an in place and in order version of the program (PFA2). These two last programs do not perform the inverse DFT. In this work ways to implement this as an option of the same program are systematically derived from the general properties of the prime factor index maps and tested.