Variable 1-D digital filter designs using vector-array decomposition

When the given variable frequency response specifications are complicated, variable one-dimensional (1-D) digital filters are very difficult to design. This paper proposes a new approach for solving the problem. The basic idea of the new approach is not to design variable 1-D filters directly, but simplify the design problem to an easier one that merely requires constant 1-D filter designs and multi-dimensional (M-D) polynomial approximations based on the newly proposed vector-array decomposition (VAD).