An analytical least square solution to the design problem of two-dimensional FIR filters with quadrantally symmetric or antisymmetric frequency response

Abstract

A closed-form least-squares solution to the design problem of two-dimensional real zero-phase finite-impulse-response (FIR) filters with quadrantally symmetric or antisymmetric frequency response is obtained. An in-depth study of the matrices involved in the development of the design technique reveals a number of useful properties. It is shown that these properties lead to an optimal analytical solution for the filter coefficients, making it unnecessary to use the time-consuming methods of optimization, matrix inversion, and iteration. Because of the reduced order of the matrices involved, their specific characteristics, and the analytical approach, the computational complexity is greatly reduced. Simplicity and efficiency of the design technique is illustrated through examples. The results in terms of error in frequency response compare favorably with those obtained by using other techniques. It is shown that the design time using the proposed technique is significantly smaller than that required by the I/sub p/-optimization technique or weighted least-squares technique using Harris' ascent algorithm or modified Lawson's algorithm. >