Analytical Synthesis of Parameter-Varying Filter of Constant Component with Application to Switching Systems

Abstract

In this paper, we propose a concept of a continuous-time filter of constant component that exhibits a very short response in the time domain if compared to the traditional time-invariant filter. The improvement of the filter dynamics was achieved as a result of the time-varying parameters which were introduced to the filter structure. Such a designed filter is then applied in a system which switches many distorted signals which should be filtered as fast as possible. The paper is of review nature and presents both a theoretical background of the proposed filter and the results of simulations.

A Variational Approach for Designing Infinite Impulse Response Filters With Time-Varying Parameters

“…The stability properties of the system with time-varying parameters are considered taking into account the discussion presented in [22], [28], [29]. In this regard, first-and secondorder systems are modeled by scalar linear time-varying differential equations.…”

“…The optimal expression is obtained through the use of the mathematical tool of calculus of variations [27], that to the best of our knowledge, had not been previously applied to this problem. The current work is inspired by the work presented in [17] and further analyzed in [22], [28], [29]. Although the proposed solution is obtained for first-and second-order systems, the generalization to higher-order filters is straightforward and can be obtained by implementing a cascade structure comprised by first-and second-order filters.…”

A Concept of the Non-Stationary Filtering Network with Reduced Transient Response

“…The results of the preceding research [13][14][15] have shown that filters with time-varying parameters work undoubtedly better in the time domain than filters with time-invariant parameters. The quality of their operation is determined by the time after which the error value of the output signal is no greater than the assumed accuracy, α.…”

Digital Finite Impulse Response Notch Filter with Non-Zero Initial Conditions, Based on an Infinite Impulse Response Prototype Filter

“…In matrix (12) vector is in the row space for any initial phase of ( ). The next step of the projection method is to define the projection operator .…”

“…The improvement of the transient response is a problem which has been considered in many fields of engineering. However, the commonly used filters are, in many cases, inappropriate due to the long duration of transients [12][13].…”