Twiddle factor merged time-decimal FFT algorithm and the software implementation for twiddle factor merged FFT algorithm

Abstract

Martens proposed a highly efficient and simply formed DFT algorithm—RCFA whose efficiency is comparable with that of WFTA or that of PFA, and whose structure is similar to that of FFT. The authors have proved that, in the case of radix 2, the RCFA is exactly equivalent to the twiddle factor merged frequency-decimal FFT algorithm. The twiddle factor merged time-decimal FFT algorithm is provided in this paper. Thus, in any case, the FFT algorithm used currently can be replaced by the more efficient algorithm—the twiddle factor merged FFT algorithm, with exactly the same external property and the similar internal structure. Also in this paper, the software for implementing the twiddle factor merged FFT algorithm (TMFFT) is provided.