Non-Abelian Fourier transform, Polar form of a matrix, Irreducible representation, Irreducible character, Amplitude and phase response, G-Circulant matrix.
In the context of the non-abelian Fourier transform, the natural extension of the amplitude and phase response to a convolution by a given filter mask are shown to be the polar decompositions of the Fourier transform matrices. A specific example regarding amplitude and phase response of a certain filter mask over the symmetric group S_3 is given.
"On the amplitude and phase response in the non-abelian Fourier transform",
Electronic Journal of Linear Algebra,
Volume 31, pp. 156-166.