A new matrix approach to real FFTs and convolutions of length 2k

Authors:
T. Lundy;J. Van Buskirk
Affiliations:
Virtuallaboratory.net, 3500 Allison Street, 80033, Wheat Ridge, CO, USA;One Room Schoolhouse of Physics, 3500 Allison Street, 80033, Wheat Ridge, CO, USA
Venue:
Computing
Year:
2007

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Abstract

A new matrix, scaled odd tail, SOT, is introduced. This new matrix is used to derive real and complex FFT algorithms for lengths n = 2 k . A compromise is reached between Fourier transform and polynomial transform methods for computing the action of cyclic convolutions. Both of these methods lead to arithmetic operation counts that are better than previously published results. A minor improvement is also demonstrated that enables us to compute the actions of Fermat prime order FFTs in fewer additions than previously available algorithms.