A weighted-least-squares matrix decomposition method with application to the design of two-dimensional digital filters

A matrix decomposition method that generates a decomposition which is similar to that produced by the singular-value decomposition (SVD) is proposed. When applied to the design of 2-D FIR or IIR digital filters, the method provides for different error weightings at each point in the frequency plane, thereby allowing for smaller errors or don´t care conditions in specified regions. When compared to the SVD, the proposed method can be better suited to the design of two-dimensional filters when using a sum-of-products realization. Examples for the design of 2-D FIR lowpass filters are given