The design of 2-D approximately linear phase filters using a direct approach

A novel approach to the design of approximately linear phase recursive digital filters was recently described. The technique exploited a property of allpass transfer functions which allowed the creation of a set of linear simultaneous equations in the filter coefficients which could then be solved in the least-squares sense. This paper extends the design method to 2-D and multi-D filters. These filters find application in many areas including image processing, image coding, filter banks and seismic data processing. Several problems arise which are not present in the 1-D design and the paper looks at ways to overcome them. In addition, there is discussion on the stability issue. Several examples including circularly, elliptically and diamond symmetric lowpass filters and a fan filter are presented. Comparison is made between the proposed technique and those of Gu and Swamy (1994) and Toyoshima et al. (1990). (C) 1997 Elsevier Science B.V.