A new Truncated Fourier Transform algorithm

TL;DR

This paper introduces an in-place Truncated Fourier Transform algorithm with complexity comparable to existing methods and presents a transformation linking different TFT families, improving efficiency and flexibility.

Contribution

It presents a new in-place TFT algorithm with similar complexity to existing methods and a transformation connecting different TFT families, enhancing algorithmic versatility.

Findings

In-place TFT algorithm with comparable complexity to existing methods.

Transformation linking different TFT evaluation point sets.

Improved efficiency and flexibility in TFT computations.

Abstract

Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in terms of ring operations, is comparable to existing not-in-place TFT methods. We also describe a transformation that maps between two families of TFT algorithms that use different sets of evaluation points.