Two‐dimensional recursive digital filters with nearly circular‐symmetric magnitude response and approximately linear phase

This paper presents a general structure using 1-D and two-dimensional (2-D) recursive digital all-pass filters (DAFs) for the design of 2-D recursive circularly symmetric digital low-pass filters (CS-DLFs). The general structure is a cascade of two stages composed of all-pass building blocks. The first stage is a parallel connection of a 2-D recursive DAF with a symmetric half-plane (SHP) support for its filter coefficients and a 2-D pure delay block. The second stage composed of a parallel connection of a 1-D recursive DAF and a 1-D pure delay block is used for eliminating the unwanted pass-band induced by the first stage. As a result, the design of a 2-D CS-DLF in either the least-squares or the minimax sense can be formulated in a simple linear optimization problem in terms of the weighted-phase response error for each DAF. Design results with nearly circularly symmetric magnitude response and approximately linear phase are also provided for illustration and comparison. Copyright © 2010 John Wiley & Sons, Ltd.