The skew spectrum of functions on finite groups and their homogeneous spaces

Whenever we have a group acting on a class of functions by translation, the bispectrum offers a principled and lossless way of representing such functions invariant to the action. Unfortunately, computing the bispectrum is often costly and complicated. In this paper we propose a unitarily equivalent, but easier to compute set of invariants, which we call the skew spectrum. For functions on homogeneous spaces the skew spectrum can be efficiently computed using some ideas from Clausen-type fast Fourier transforms.