Decomposition-based design of linear phase variable digital filters

Variable digital filters are especially difficult to design when the given variable design specifications are complicated. The author proposes a new method for designing variable one-dimensional (1-D) digital filters approximating both the given variable magnitude responses and linear phase (constant group delay) responses. The basic idea of the method is to reduce the difficult problem of directly designing a variable filter to the problem that only requires the design of the normal constant 1-D filters and 1-D polynomial approximations. To do so, we first propose a method for decomposing the given complex-valued variable design specifications into constant 1-D frequency response specifications and 1-D polynomial specifications. Then the resulting 1-D specifications are individually approximated, which is easy to do. Consequently, the original variable filter design problem can be easily solved.