Improved QFT algorithm for power-of-two FFT

TL;DR

This paper presents an improved QFT algorithm for power-of-two FFT that reduces trigonometric constants and maintains computational efficiency, enhancing accuracy and memory use while introducing a new descriptive notation.

Contribution

It introduces a slight modification to the QFT algorithm that halves the trigonometric constants needed, matching the efficiency of split-radix FFT, and proposes a new notation for describing FFT algorithms.

Findings

Same number of operations as split-radix 3add/3mul

Uses half the trigonometric constants

Improves accuracy and memory efficiency

Abstract

This paper shows that it is possible to improve the computational cost, the memory requirements and the accuracy of Quick Fourier Transform (QFT) algorithm for power-of-two FFT (Fast Fourier Transform) just introducing a slight modification in this algorithm. The new algorithm requires the same number of additions and multiplications of split-radix 3add/3mul, one of the most appreciated FFT algorithms appeared in the literature, but employing only half of the trigonometric constants. These results can elevate the QFT approach to the level of most used FFT procedures. A new quite general way to describe FFT algorithms, based on signal types and on a particular notation, is also proposed and used, highligting its advantages.