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

Abstract

The SVD has been applied in conjunction with 1-D FIR-filter techniques for the design of 2-D quadrantally-symmetric FIR filters. It has been shown that three related realizations are possible and in each case, causal, linear-phase designs can easily be obtained. Each realization consists of a number of parallel 1-D filters and, therefore, fast designs are possible which are suitable for real-time or quasi-real-time application.

The modified SVD realization is more efficient than the direct SVD realization and, in turn, the SVD-LUD realization is more efficient than the modified SVD realization. The last two methods have the important advantage that the number of parallel sections, and hence the number of multiplications, dose not increase as more singular values are included in the design. Consequently, the approximation error introduced by the application of the SVD can be reduced to an insignificant level.

Some examples based on the application of 1-D window techniques have shown that our method leads to very good designs with low computational effort.