Design of 2-D digital filters with arbitrary amplitude and phase responses by using the singular value decomposition

The SVD (singular value decomposition) method is extended to include the design of FIR (finite impulse response) and IIR (infinite impulse response) 2-D filters with arbitrary amplitude and phase responses. The design starts by sampling the desired frequency response in order to generate a complex matrix that represents both the amplitude and the phase responses. The SVD is then applied to this matrix to obtain an outer-product sum expression. It is shown that each vector in an outer-product term can be interpreted as the frequency response of a 1-D digital filter and therefore the design task can be completed if methods for the design of 1-D digital filters with arbitrary amplitude and phase responses are available. Two such methods for the design of 1-D FIR filters based on least-squares and least-pth optimization are presented. The proposed method is relatively simple to apply and leads to a parallel arrangement of pairs of cascaded 1-D filter sections. Structures of this type allow a large amount of concurrent processing and, further, they can be implemented in terms of systolic arrays. Therefore. they are amenable to VLSI implementation