Magnitude Approximation of 2-D IIR Filters

Abstract

In this chapter, we describe several methods for the design of two-dimensional (2-D) IIR digital filters, which have passbands and stopbands defined by regions in the ω1 — ω2 plane. For the design of 1-D IIR filters, typically the given specifications are (1) the type of filters (e.g. lowpass,bandpass) (2) the type of response in the passband and stopbands (e.g. maximally flat or equiripple) (3) the cutoff frequency ωc defining the passband and the maximum attenuation A p (or ripple in dB) in the passband (4) the stopband cutoff frequency ωs and the minimum attenuation A s in the stopband and so on. For the design of 2-D IIR filters, an additional specification is the shape of the passband and stopband regions in the ω1 — ω2 plane instead of the cutoff frequencies ωc and ωs. This additional specification makes a significant difference in the methods for designing 2-D filters in the sense that when all the other specifications are the same, the design methods will be different if the passband and stopband regions are different. Some of the common types of regions are those bounded by straight lines and the methods for the design of such filters are discussed in sections 3.2 and 3.3 of this chapter. Another type of passband and stopband are circular or elliptical regions in the ω1 —ω2 plane. In section 3.4, a few well-known methods for the design of filters with circular passband or stopband regions in the ω1 — ω2 plane are discussed. Once such filters are designed, it is easy to design filters with new shapes and in different part of the frequency plane. For example, using some spectral transformations [6, 25] digital filters with an elliptical passband or stopband can be obtained, from the design of circularly symmetric lowpass filters. These spectral transformations will be considered at the end of the chapter.KeywordsTransfer FunctionLowpass FilterDigital FilterMagnitude ResponsePrototype FilterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.