SVD-based theorem for designing arbitrary-phase variable filters

Arbitrary desired variable frequency response could be uniformly sampled to construct a multi-dimensional (M-D) complex array. This paper proposes a new method called vector-array decomposition (VAD) for decomposing 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 sub-problems that require one-dimensional (1-D) constant filter designs and M-D polynomial approximations, thus variable filters can be indirectly designed through solving the easier sub-problems.