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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>