Properties of the Two-Sided RMF Spectrum of Matrices

Abstract

The Reed-Muller-Fourier transform, defined in a q-valued domain, is applied to obtain two-sided spectra of classes of matrices, which may be interpreted as representing pixels of pictures or patterns. Operations on matrices, representing operations on pictures are considered, and their effect in the spectral domain is analyzed. It is shown that the transform is very effective to calculate the spectrum of mosaics and is sensitive to the existence and position of a pixel-noise. Moreover, there are some matrices which are fixed points of the transform.