Recent Progress and Applications in Group FFTs

2006/01/27 by Daniel N. Rockmore · 1 citation
Mathematics · Computer Science · #Mathematical Analysis and Transform Methods #Digital Filter Design and Implementation #Algebraic and Geometric Analysis

paper · doi:10.1007/1-4020-2307-3_9

openalex publication_date 2006/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

The Cooley-Tukey FFT can be interpreted as an algorithm for the effcient computation of the Fourier transform for finite cyclic groups, a compact group (the circle), or the non-compact group of the real line. These are all commutative instances of a “Group FFT.” We give a brief survey of some recent progress made in the direction of noncommutative generalizations and their applications.

Citations

• Efficient Quantum Transforms
• A fast transform for spherical harmonics
• The Chirp z-Transform Algorithm and Its Application
• An algorithm for the machine calculation of complex Fourier series
• Fast Fourier Transforms
• Gauss and the history of the fast Fourier transform
• On the Power of Quantum Computation
• The Hidden Subgroup Problem in Affine Groups: Basis Selection in Fourier Sampling
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• Generic Quantum Fourier Transforms
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Cited by

• Fast Fourier transform [wikipedia]