Approximately linear-phase recursive digital filters with variable magnitude characteristics

This paper considers designing in the minimax sense complementary low-pass/high-pass approximately linear-phase recursive filters with variable magnitude characteristics. A filter structure based on the parallel connection of a delay and a variable fractional delay all-pass filter is proposed for implementing these filters. The filter optimization is performed in two basic steps. First, an initial filter is generated using a simple design scheme. Second, this filter is used as a start-up solution for further optimization being carried out by an efficient constrained nonlinear optimization algorithm. Examples are included for illustrating the efficiency of the proposed design scheme. In addition, the performance and the complexity of the proposed variable recursive digital filters are compared with those of the other variable recursive digital filters proposed in the literature. This comparison shows that the number of multipliers for the proposed filters is less than 30 percent compared with the other existing structures