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

Author

Clausen, Michael and Kakarala, Ramakrishna

Subjects
Homogeneous space, Symmetric group, Discrete Fourier transform, FFT, Fast convolution
Abstract

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.

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