On Fixed Points of the Reed-Muller-Fourier Transform

The Reed-Muller-Fourier transform combines relevant aspects of the RM transform and the DFT. It constitutes a bijection in the set of p-valued functions. Some properties of the transform matrix are formally analyzed and its eigenvectors with eigenvalue lambda = 1, which are its fixed points, are studied. Some methods to generate fixed points from known fixed points are presented and the number of fixed points for some values of p and n are given.