Analysis and Synthesis of the Digital Structures by the Matrix Method

Abstract

This paper presents a general matrix algorithm for analysis of digital filters. The method proposed in this paper allows not only the analysis of the digital filters, but also the construction of new structures of the canonic or non-canonic digital filter. Equivalent filters of different structures can be found according to various matrix expansions. The structures can be calculated even from transfer function or from state-space matrices and with the additional advantage of requiring minimum number of shifting elements. Traditional research methods are not able to construct the system with a minimum of the shifting operations.