A direct approach to the design of multidimensional PCAS digital filters satisfying gain and group delay specifications simultaneously

Digital filters with linear or almost linear phase are required in many applications including video, sonar and image processing. A direct design approach is reported here which can be applied to 1-D and M-D filter design so long as the filter structure is a parallel combination of allpass subfilters (PCAS). PCAS filters are used because of their low complexity and roundoff noise as well as their ability to realise non-minimum phase transfer functions. The filter design will be shown to reduce to the solution of two sets of linear simultaneous equations. Examples are given in both the 1-D and 2-D case to illustrate the method