Design of two-dimensional FIR digital filters with specified magnitude and group delay responses by analytical least-squares method

In this paper, an analytical least-squares approach to the design of quadrantally symmetric 2-D filters is extended to design complex-coefficient 2-D FIR filters with arbitrary complex frequency responses. Given the design specifications, the filter coefficients are determined directly from a closed-form transformation matrix, such that time-consuming optimization, matrix inversion and iteration procedures can be avoided. Several examples are presented to demonstrate the simplicity and effectiveness of the proposed method.