MATHEMATICAL MODELLING OF SYSTEM FUNCTIONS BASED ON LINEAR DIFFERENCE EQUATIONS FOR STABILITY, CAUSALITY AND INVERSE ANALYSIS

摘要

The digital data processing and digital communication sectors have conducted extensive research aimed at both accuracy and computational time to meet the increasing demands from industry. One of the most fundamental and accurate mathematical procedures for modeling DT-LTI (Discrete Time - Linear Time Invariant) systems is based on the Z-Transform and DTFT (Discrete-time Fourier Transform). In this paper we investigate the concepts underlying the system spectrum characteristics in both the Z-Transform and DTFT domains to provide analysis for stability and causality in terms of the pole-zero complex plain. We explore the procedures through case studies and illustrate the results in both pictorial and mathematical data forms to clarify the concepts.