Design of complex-coefficient variable digital filters using successive vector-array decomposition

Singular-value decomposition (SVD) can be efficiently utilized to obtain the optimal vector-array decomposition (VAD) for simplifying real-coefficient variable digital filter design problem, but the SVD-based VAD methods are not applicable to the design of complex-coefficient variable filters. This paper proposes a successive algorithm for decomposing arbitrary multidimensional complex array into the VAD form, and thus, a complex-coefficient variable digital filter with arbitrary variable frequency response can be easily obtained through constant complex-coefficient filter design and multidimensional polynomial fitting. The new VAD algorithm successively decomposes the complex array and its residual arrays into the vector-array pairs stage by stage, and each stage contains an iterative optimization that can be easily solved in a closed-form. Our computer simulations have demonstrated that the successive VAD converges very fast to the optimal solution.