Vector-array decomposition-based design of variable digital filters

Arbitrary desired variable frequency response can be uniformly sampled to construct a multi-dimensional (M-D) complex array. In this paper, we propose a new method called vector-array decomposition (VAD) for decomposing the M-D complex array into the products of complex vectors and real arrays. Based on the VAD, the difficult problem of designing variable digital filters can be reduced to some easier subproblems that require one-dimensional (1-D) constant filter designs and M-D polynomial approximations. Since 1-D constant filters can be easily obtained by applying the well developed design techniques, and M-D polynomials can be obtained by utilizing least-squares curve-fitting, variable filters can be indirectly designed through solving the easier sub-problems. The VAD-based approach is straightforward and particularly efficient for designing variable filters with arbitrary variable magnitude responses and arbitrary phases.