SVD-based design of fractional-delay 2-D digital filters exploiting specification symmetries

An attractive approach to the design of two-dimensional (2-D) digital filters is to decompose the original difficult 2-D design problem into a set of relatively easier subproblems that involve one-dimensional (1-D) filter designs. Lu et al. have shown that the design technique using the singular value decomposition (SVD) can be applied to the design of 2-D filters with arbitrary magnitude and phase responses. The most important point of this paper is to show that some magnitude and phase symmetries can be efficiently exploited in the SVD-based designs, which can reduce the computational complexity and save the computer storage required for 1-D filter (subfilter) coefficients by 50%. Moreover, an objective criterion is proposed for selecting the appropriate subfilter orders in order to reduce the hardware implementation cost. A fractional-delay 2-D filter is designed to illustrate the effectiveness of the SVD-based approach by exploiting the specification symmetries and new order-selecting criterion.