Nima Bayan

Frequency analysis of linear time-varying systems

This paper outlines a solution technique developed for frequency-domain analysis and synthesis of linear time-varying (LTV) systems. By an application of two-sided Laplace transform and two-dimensional Laplace Transform (2DLT), in general, the frequency-domain techniques are developed, which facilitate the analysis or synthesis of variable and adaptive systems. The significant advantage of the frequency analysis and synthesis over the time-domain techniques is clear.

Frequency analysis of linear time-varying systems: a new perspective

This paper extends the application of Laplace transform as a frequency-domain tool of linear time-invariant (LTI) systems to the analysis and synthesis of linear time-varying (LTV) systems. It is shown that the LTV system input and output are related to each other by their bi-frequency transfer function H (s1, s2). This is the two-dimensional Laplace transform (2DLT) of the unit-impulse response of the system. The LTI systems and other transformation techniques can be considered as special cases of this general method. On the basis of the results presented in this paper, applicability of the Laplace transform to linear ordinary differential equations (ODE) as well as general linear systems is verified. This is on the contrary to a hitherto-known belief that confined the use of Laplace transform to LTI systems only

On properties of double laplace transformation for analysis of linear time-varying systems

Properties of double (or two-dimensional) Laplace transform (2DLT) for analysis of linear time-varying (LTV) systems are explored. The one-dimensional to two-dimensional expansion formulas, as well as the two-dimensional to one-dimensional reduction formulas, are outlined. The merit of the proposed technique for frequency analysis of LTV systems is demonstrated.

A note of frequency-domain characterization of linear time-varying networks

The extension of the Laplace transform techniques for characterization of linear time-varying (LTV) networks is presented. The proposed two-dimensional Laplace transform (2DLT) can be used as a framework for analysis and synthesis of LTV networks and systems that exhibit a circular symmetry property.

Frequency-domain realization of linear time-varying systems by two-dimensional Laplace transformation

The objective of this paper is to extend application of Laplace-Carson transform (LCT) to the realization of linear time-varying (LTV) systems. We propose using the unilateral and bilateral two-dimensional Laplace transform (2DLT) for realization of LTV systems, which exhibit a circular symmetry. Application of two-dimensional Laplace and Fourier transforms to LTV systems results in a bifrequency realization. In particular, it is shown that the 2DLT of LTV systems is, in fact, a Hankel transform of order zero.

Laplace transform approach to analysis and synthesis of bessel type linear time-varying systems

Two-dimensional Laplace transform (2DLT) is applied as a powerful analysis and synthesis tool for linear time-varying networks resulting in Bessel type linear ordinary differential equations. In this sense a parallel and more powerful closed-form solution (compared to traditional transforms) is obtained which is analogous to that in which one-dimensional Laplace transform is used for linear time-invariant (LTI) systems.

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

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 bi-frequency theory for autonomous dynamic systems. The contents of existing literature are complemented more than duplicated.

Characterisation of nonlinear and linear time-varying systems by Laplace transformation

In this article we elaborate on various characterisations of nonlinear systems. Specifically, we focus on the frequency-domain characterisation of the class of single-input single-output (SISO) linear time-varying (LTV) systems. We use the model introduced by Wiener using Volterra functional and later elaborated by others. The application of the multidimensional Laplace transform (MDLT) method as a fundamental tool in analysing variable systems and understanding system dynamic behaviours is emphasised. In particular, applications of double or two-dimensional Laplace transform (2DLT) for the analysis and synthesis of LTV circuits and systems are detailed. Examples worked out that illustrate the method and demonstrate its validity in the frequency-domain.

On linear time-varying system characterizations

An alternative approach for characterization of linear time-varying (LTV) systems in the time-domain and frequency-domain is developed. The two-dimensional Laplace transform (2DLT) technique for obtaining the response of LTV systems and networks is outlined.

Frequency Analysis of Time-Varying Systems

A method of frequency analysis is presented that can be used to determine the response of time-varying systems. The method is based on Laplace transformation of functions. As a result, the homogenous solution of ordinary linear differential equations with variable coefficients is obtained. The method is used for frequency analysis and design of variable networks. The extension to nonlinear systems is possible