On the design transitional Legendre–Butterworth filters

Abstract

This paper presents a new method of the polynomial transfer function approximation both in the analog and the digital domain for the recursive digital filter design. The transfer function of these filters, referred as the transitional Legendre–Butterworth (TLB) filters, has properties that lie between Legendre and Butterworth filters. The so-designed TLB filters exhibit non-equiripple passband and monotonic transition and stopband responses. There are three types of TLB IIR filters which can be approximated in the digital domain. The closed form expressions for the magnitude squared functions coefficient of all types of transfer functions are provided, and a straightforward design technique for each approximation in the digital domain is described. Resulting digital filters are always stable.