A Matrix Laurent Series-based Fast Fourier Transform for Blocklengths N=4 (mod 8)

TL;DR

This paper introduces a novel FFT algorithm based on matrix Laurent series for blocklengths of the form 8m+4, achieving lower multiplicative complexity for certain lengths.

Contribution

It presents a new Laurent series-based FFT method that reduces multiplicative complexity for specific blocklengths, notably N=64.

Findings

Achieved lower multiplication counts than previous FFTs for N=64.

Provides detailed algorithms for N=8m+4 with m=1 and m=2.

Offers general guidelines for efficient FFT computation for these lengths.

Abstract

General guidelines for a new fast computation of blocklength 8m+4 DFTs are presented, which is based on a Laurent series involving matrices. Results of non-trivial real multiplicative complexity are presented for blocklengths N=64, achieving lower multiplication counts than previously published FFTs. A detailed description for the cases m=1 and m=2 is presented.