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.

• Type: Journal
• Year: 2010
• Where: APPML
• Authors: Michael Clausen, Ramakrishna Kakarala
• Keywords: APPML 2010, Fourier Transforms, Stabilizer Subgroup, Symmetric Group