ABSTRACT
The most serious problem in applying optimization methods for the design of non-recursive filters relates to the fact that these filters have low selectivity. This chapter begins with a study of some general symmetry properties of 2-D non-recursive filters. Then a minimax optimization method for the design of linear-phase non-recursive filters due to Charalambous is described. The second half of the chapter deals with application of the singular-value decomposition (SVD) method for the design of linear-phase non-recursive filters with arbitrary amplitude responses. In the design of recursive filters by means of the SVD, high selectivity can be achieved by using low-order recursive designs for the parallel 1-D sub-filters. The chapter shows that the SVD of the sampled frequency response of a 2-D digital filter with real coefficients possesses a special structure: every singular vector is either mirror-image symmetric or anti-symmetric about its midpoint.
