ABSTRACT
Two-dimensional (2-D) digital filters find applications in many fields such as image processing and seismic signal processing. Design of 2-D digital filters is more complicated than 1-D digital filters because of the increase in the number of coefficients with the increase in the dimension and also the difficulty of testing their stability. Fortunately, 2-D frequency responses possess many types of symmetries and the presence of these symmetries can be used to reduce the complexity of the design as well as the implementation of these filters. Symmetry in a frequency response induces certain constraints on the coefficients of the filters, which in turn reduces the filter design complexity. Therefore, a study of the symmetries of the filter frequency responses and the resulting constraints on the filter coefficients is undertaken in this chapter. As there is a close relation between digital and analog filter functions, symmetry properties are discussed in this chapter for both analog and digital domain functions. In the following, symmetries are defined, the symmetry constraints on polynomials are derived, procedures to design 2-D filters employing symmetry constraints are presented, and finally several examples are presented to illustrate the application of symmetry-based design procedure.
