, Volume 80, Issue 1, pp 23–45

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


  • J. Van Buskirk
    • One Room Schoolhouse of Physics

DOI: 10.1007/s00607-007-0222-6

Cite this article as:
Lundy, T. & Van Buskirk, J. Computing (2007) 80: 23. doi:10.1007/s00607-007-0222-6


A new matrix, scaled odd tail, SOT, is introduced. This new matrix is used to derive real and complex FFT algorithms for lengths n = 2k. 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.

AMS Subject Classifications



Fast Fourier transformsreal convolutionsRader's method
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© Springer-Verlag Wien 2007