ABSTRACT

In this chapter, methods of designing two-dimensional (2-D) finite-extent impulse response (FIR) discrete-time filters are described. Two-dimensional FIR filters offer the advantages of phase linearity and guaranteed stability, which makes them attractive in applications. Over the years an extensive array of techniques for designing 2-D FIR filters has been accumulated [14, 30, 23]. These techniques can be conveniently classified into the two categories of general and specialized designs. Techniques in the category of general design are intended for approximation of

arbitrary

desired frequency responses usually with no structural constraints on the filter. These techniques include approaches such as windowing of the ideal impulse response [22] or the use of suitable optimality criteria possibly implemented with iterative algorithms. On the other hand, techniques in the category of special design are applicable to restricted classes of filters, either due to the nature of the response being approximated or due to imposition of structural constraints on the filter used in the design. The specialized designs are a consequence of the observation that commonly used filters have characteristic underlying features that can be exploited to simplify the problem of design and implementation. The stopbands and passbands of filters encountered in practice are often defined by straight line, circular or elliptical boundaries. Specialized design methodologies have been developed for handling these cases and they are typically based on techniques such as the transformation of one-dimensional (1-D) filters or the rotation and translation of separable filter responses. If the desired response possesses symmetries, then the symmetries imply relationships among the filter coefficients which are exploited in both the design and the implementation of the filters. In some design problems it may be advantageous to impose structural constraints in the form of parallel and cascade connections.