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

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Abstract
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.<>

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