Abstract
In the design of IIR digital filters, the method that utilizes the classic analog filter design theory to design analog filters and then obtain the corresponding digital filters by sโz transformation is wellโknown. However, IIR digital filters obtained via the bilinear sโz transformation have just equalโorder numerator and denominator. Having unequalโorder numerator and denominator will give more degrees of freedom in filter design. In this paper, we consider the design of IIR digital filters with unequalโorder numerator and denominator, and propose a method for designing the flat passband and equiripple stopband filters in zโdomain directly. First, we present a design method of IIR filters with flat stopband and equiripple passband responses. The flat stopband response can be easily obtained only by locating multiple zeros on the specified frequency points, while the equiripple passband response can be designed by using the Remez exchange algorithm and specifying the maximum magnitude error. Second, we can obtain IIR filters with flat passband and equiripple stopband responses via a magnitude transformation such that the passband and stopband become the corresponding stopband and passband, respectively. However, the numerator order of IIR filters obtained by the above method is equal to or higher than the denominator. Finally, we consider the design of IIR filters that have lowerโorder numerator than denominator, and present a method for designing the flat passband and equiripple stopband filters directly. ยฉ 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(11): 37โ44, 2001