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

Abstract

Filter design with short transient state is a problem encountered in many fields of circuits, systems and signal processing. In this paper a novel low-pass filter design technique with time-varying parameters is introduced in order to minimize the rise-time parameter. Through the use of calculus of variations a method is developed to obtain the optimal closed-form expression for adjusting the parameters. In this context, two cases are addressed. The ideal case in which infinite bandwidth is required and a solution of finite bandwidth. The latter is obtained by means of a proper constraint formulation in the frequency domain. The proposed filter achieves the shortest rise-time and allows better preservation of the edge shape in comparison with other existing filtering methods. The analysis, synthesis and performance of the proposed system is discussed and illustrated with the aid of simulations.Index Terms-Filter design, rise-time, time-varying parameters, calculus of variations.

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