Design of two-dimensional digital filters using singular-value decomposition and balanced approximation method

It is shown that singular-value decomposition (SVD) can be applied along with 1-D finite-impulse-response (FIR) techniques to design linear-phase 2-D filters with arbitrary prescribed amplitude responses that are symmetrical with respect to the origin of the (ω₁ , ω₂) plane. the balanced approximation method is applied to 2-D linear-phase FIR filters of the type obtained by the SVD method. The method leads to economical and computationally efficient filters, usually IIR filters, which have prescribed amplitude responses and whose phase responses are approximately linear