A novel approach for designing linear-phase variable two-dimensional (2-D) digital filters is described, which is based on the matrix-array decomposition (MAD) of real-valued multidimensional (M-D) arrays. By using the MAD, the desired variable 2-D magnitude response can be decomposed into the real-valued frequency response specifications of the normal constant 2-D filters and the approximation specifications of M-D polynomials. Thus the problem of designing a variable 2-D filter can be decomposed into the sub-problems that involve the design of constant 2-D filters and the approximation of M-D polynomials. Since the sub-problems are much easier to solve than the direct approximation of the given variable 2-D magnitude response specification, this MAD-based design approach is extremely efficient and straightforward.
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