Inversion of Shortened LDI Matrix for Designing Discrete-time Filters

Abstract

The paper deals with the problem of the inversion of the so-called shortened LDI matrix for conversion between the coefficients of continuous-time and discrete-time linear filters whose s- and z-domain transfer functions are coupled via LDI transform. The elements of the inverse matrix are expressed by analytic formulae for general order of the matrix. The corresponding mathematical proofs are given.