A new variant of Radix-4 FFT

Abstract

Rader abd Brenner's `real-factor' FFT can be applied to Radix-4 FFT to fetch saving in the multiplication counts. However in turn the number of addition count increases which results in increase in total flop count. For this in this paper two levels of saving ideas are proposed. First is a slight modification to Rader and Brenner's `real-factor' FFT for Radix-4, which not only reduces the multiplication but also makes the total flop count equals to standard Radix-4 FFT. Second is to apply the scaling operation to the Twidlle Factors(TF) similar to Tangent FFT like one proposed by Frigo for split radix so that the net computational complexity is of the order of 4Nlog2N computation, where N is the size of FFT. As such the complexity order is same as Standard Split Radix FFT.