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

Abstract

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 (s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ). 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