Design of IIR Digital Filters with Flat Passband and Equiripple Stopband Responses

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 s–z transformation is well-known. However, IIR digital filters obtained via the bilinear s–z transformation have just equal-order numerator and denominator. Having unequal-order numerator and denominator will give more degrees of freedom in filter design. In this paper, we consider the design of IIR digital filters with unequal-order numerator and denominator, and propose a method for designing the flat passband and equiripple stopband filters in z-domain 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 lower-order numerator than denominator, and present a method for designing the flat passband and equiripple stopband filters directly. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(11): 37–44, 2001