Minimization of Haar wavelet series and Haar spectral decision diagrams for discrete functions

In this paper, a minimization of Haar wavelet series for simplification of circuits and Haar based decision diagrams representing discrete multiple-valued functions is proposed. The minimization is performed by permutation of indices of generalized Haar functions. Experimental results show that this method provides reasonable reduction in the number of non-zero coefficients. The Haar series reduced this way can be useful in the circuit synthesis for realization of multiple-valued functions. The same algorithm can be also used to reduce the number of paths in decision diagrams related to the Haar wavelet transforms. In many cases, this reduction provides smaller size of such decision diagrams.