A unified expression for split-radix DFT algorithms

This paper presents a unified expression that covers all previously reported split-radix-2/2
^m
, where m is an integer larger than one, algorithms. New split-radix algorithms can be also derived from this unified expression. These algorithms flexibly support DFT sizes N = q · 2
^r
, where q is generally an odd integer. Comparisons show that the computational complexity required by the proposed algorithms for the DFT size N = q · 2r is generally not more than that for the DFT size N = 2
^r
. In particular, our examples show that the split-radix-2/4 algorithm requires a smaller computational complexity compared to other split-radix algorithms and the prime factor algorithms.