Analysis of linear time-varying circuits by two-dimensional analog filtering

Abstract

Our focus is on the frequency analysis of LTV systems within the larger context of 2-D analog filtering. The available techniques for characterizing 2-D analog filters are explained. The frequency analysis of 2-D analog systems, based on the classical two-dimensional Laplace transform (2DLT), is outlined. The 2DLT leads to the development of a bifrequency theory for autonomous dynamic systems. The contents of existing literature are complemented more than duplicated.

Two-dimensional analog signal processing and its implications on circuit theory

“…More information about 2-D singularity functions and their applications can be found in [4] and [14].…”

“…: Expression (22) is said to be the 1st-degree impulse-response function of a 2nd-degree impulse-response function of h 2 t; s ð Þ. The 1st-degree impulse-response function for physical bivariate systems is called the general initial condition [4]. Other particular initial conditions may be defined corresponding to cases when either t ¼ 0 or s ¼ 0 or both t and s are equal to zero.…”

“…The objective of this note is to complement, with least possible duplication, work in the bivariate analog system theory and treatment of linear time-varying (LTV) systems reported earlier [4]. Naturally, some repetition is unavoidable for a coherent and comprehensive presentation.…”