Abstract

The present thesis is concerned with design techniques for two-dimensional zero-phase finite impulse response digital filters with nonuniform frequency samples. Using the freedom and flexibility of the nonuniform frequency sampling, several techniques for taking samples in the frequency plane have been proposed. The design problem is treated as a bivariate interpolation problem with unevenly spaced data. The main idea is to select (find) sampling locations in the (} 1 , } 2 ) frequency plane and corresponding sample values H d (} 1k , } 2k ) of the desired filter frequency response such that the approximation error in the designed filter is reduced significantly and the shape performance is high. Three main types of two-dimensional zero-phase FIR filters that are most frequently used in practice have been considered: rectangular, circular, and 2-D halfband (diamond and fan) FIR filters. At least two sampling techniques for each filter type have been proposed and examined. Common features of all of the proposed sampling approaches are that the design is performed entirely with real number arithmetic, no computationally expensive iterative procedures are used, and the samples are taken on curves that match the contours of the desired filter frequency response magnitude,. Although the filters designed with the proposed techniques are not optimal (in strict sense), the methods are conceptually simple and produce filters with high degree of shape regularity and approximation error comparable and sometimes even smaller than the "conventional" 2-D FIR filter design methods.