Analysis of a class of LTV systems by differential operator with time-varying coefficients and its frequency localizable transform Kernel for instantaneous frequency identification

Abstract

In this dissertation, the eigenstructure of a class of linear time-varying systems, termed as linear quasi-time invariant (LQTI) systems, is investigated. A system composed of dynamic devices such as linear time-varying capacitors and resistors can be an example of the class. Naturally, in case that the capacitors and resisters are manufactured in the same processes with the same materials respectively, the time-varying property due to the thermal characteristics remains almost the same. Also, external electromagnetic field has an effect on analog monolithic integrate circuit. Because of the fact that the plates of capacitor are a heavily doped semiconductor rather than an ideal conductor, some variation in surface potential relative to the bulk material of the plate occurs as external field is applied to the poly-poly capacitor. Then, variation of capacitance and resistance caused by external time-varying field is the same for each component. At first, in order to describe and analyze the LQTI systems, a differential operator G composed of the derivative operator D and some time functions is adopted. Then, the dynamic systems described by the operator G are studied in terms of eigenvalue, frequency characteristics, stability and an extended convolution. Some basic attributes of the operator G are compared with those of the differential operator D. The corresponding generalized Laplace transform pair is defined and relevant properties are derived for frequency domain analysis and design of the LQTI filters. It is also noted that the stability is determined by the position of poles in the G frequency domain, where the stable region in the complex plane is different from the classical left half s-plane. A point in the extended Laplace transform space represents a complex exponential function modulated by some time-varying functions. As an application example, an LQTI filter is examined and designed by using the concept of eigenstructure of LQTI system. Secondly...