Design of two-dimensional FIR digital filters by using the singular-value decomposition

Singular-value decomposition (SVD) is applied to the design of two-dimensional (2-D) FIR (finite-impulse-response) digital filters. It is shown that three realizations are possible, namely, a direct realization, a modified version of direct realization, and a realization based on the combined application of SV and LU decomposition. Each of the realizations consists of a parallel arrangement of cascaded pairs of 1-D filters; hence extensive parallel processing and pipelining can be applied. The 1-D FIR filters can be designed using standard methods, and linear-phase causal 2-D filters that are suitable for real-time or quasi-real-time applications can also be designed. The three realizations are compared, and it is shown that the realization based on combined SV and LU decomposition leads to the lowest approximation error and involves the smallest number of multiplications. SVD, the McClellan transformation, and 2-D window design methods are used to design a bandpass and a fan filter, and the results are compared