Ternary Haar-like transform and its application in spectral representation of ternary-valued functions

Abstract

The paper introduces a signal adaptive Haar-like transform for ternary functions. The term adaptive means, given the signal, we design a transform after a brief analysis of signal features such as appearance of identical patterns or periods of constancy. The proposed transform possesses a fast FFT-like computation algorithm similar to fast algorithms for the classical Haar transform on finite dyadic groups as well as the generalized Haar transforms for multiple-valued functions. The proposed transform is utilized in reduction of the number of nonzero coefficients in spectral representation of ternary functions. The method shows good results, especially, when the given ternary signal contains intervals of constancy or repeated patterns having relatively high frequency of appearance.