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2010

Computing Fourier transforms and convolutions of Sn-1-invariant signals on Sn in time linear in n

13 years 3 months ago
Computing Fourier transforms and convolutions of Sn-1-invariant signals on Sn in time linear in n
Let Sn denote the symmetric group on {1, . . . , n} and Sn-1 the stabilizer subgroup of n. We derive algorithms for computing Fourier transforms of left and right Sn-1-invariant signals a : Sn C that require a total of 2n-2 additions and n - 2 scalar multiplications. Furthermore we show that the convolution of such signals can also be computed in time linear in n. Key words: Symmetric group, homogeneous space, discrete Fourier transform, FFT, fast convolution.
Michael Clausen, Ramakrishna Kakarala
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2010
Where APPML
Authors Michael Clausen, Ramakrishna Kakarala
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