Time-frequency responses of generalized first order parametric sections

Abstract

This paper presents the method of analysis of parametric systems in frequency domain. These systems are also referred to as linear time varying systems (LTV). The article includes a description of an analytical method for determining the frequency response of the first order parametric circuit with non-periodically variable parameters. The results have been illustrated by an example.

Archives of Electrical Engineering

“…Moreover, the works e.g. [4,5], show that for such a selection of exponentially varying coefficients it is possible to determine parametric solutions of differential equations describing the LTV systems and to present an impulse response in an analytically closed form as well as a response to any excitation of such a system. There are some papers e.g.…”

“…There are known works focused on the theoretical analysis in the time and in the frequency domain [1,4,[7][8][9]. The continuous time-varying system can be treated as an auxiliary tool for analysis of fractional systems [10].…”

Modelling of the First-Order Time-Varying Filters with Periodically Variable Coefficients

“…The functions ( , ) and ( , ) are called transfer functions or frequency characteristics of LTV systems [1,37,38]. They are very helpful representations used in the LTV system theory [5,36,39].…”

“…The transfer function and the frequency response for LTV systems can be defined in various ways [1,12,[36][37][38]. The most popular definitions have been given below:…”