Abstract

Digital filter design with short transient state is a problem encountered in many fields of 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 methodology is developed to write down the optimal closed-form expression for varying the parameters. In this concern, two cases are addressed. The ideal case in which infinite bandwidth is required and a solution of finite bandwidth. The latest is obtained by means of a proper restriction in the frequency domain. The proposed filter achieves the shortest rise-time and allows better preservation of the edge shape in comparison with other reported filtering methods. The performance of the proposed system is illustrated with the aid of simulations.