On stationary linear time-varying systems

TLDR

The paper reviews representations of linear time‑varying systems and introduces stationary systems, extending the theory to discrete‑time and hybrid contexts. The authors define stationary deterministic signals, characterize stationary systems via spectral relations, analyze causality constraints, and extend the framework to discrete‑time and hybrid systems. The study shows that stationary systems have a simpler spectral input‑output relation, that causality imposes strict constraints on realizable frequency mappings, and provides examples such as decimators, periodic samplers, bilinear A/D converters, and analyzes a generalized sampling method.

Abstract

A comprehensive review of representations of linear timevarying systems is given, both in the time and in frequency domains. Subsequently a definition is given of a stationary deterministic signal. Based on this definition the notion of stationary systems is introduced. These systems have the useful property that the spectral relation between input and output has a simpler form than the corresponding relation for arbitrary time-varying systems. It is shown that causality puts rather severe constraints on the frequency mappings that can be realized by stationary linear systems. An extension of the theory of linear time-varying systems to the case of discrete-time and hybrid systems (analog input, digital output, or vice versa) is discussed. Examples of stationary systems are given, such as a decimator, a periodic sampler, and a bilinear A/D converter. Also, a recently proposed generalized sampling method is analyzed by means of the concepts discussed in this paper.