High-speed recursive digital filters based on the frequency-response masking approach

The frequency-response masking approach for highspeed recursive infinite-impulse response (IIR) digital filters is introduced. In this approach, the overall filter consists of a periodic model filter, its power-complementary periodic filter, and two masking filters. The model filters are composed of two all-pass filters in parallel, whereas the masking filters are linear-phase finite-impulse response (FIR) filters. The transfer functions of the all-pass filters are functions of z^M , which implies that the maximal sample frequency for the overall filter is M times that of the corresponding conventional IIR filter. The maximal sample frequency can be increased to an arbitrary level for arbitrary bandwidths. The overall filter can be designed by separately optimizing the model and masking filters with the aid of conventional approximation techniques. The obtained overall filter also serves as a good initial filter for further optimization. Both nonlinear-phase and approximately linear-phase filters are considered. By using the new approach, the potential problems of pole-zero cancellations, which are inherent in algorithm transformation techniques, are avoided. Further, robust filters under finite-arithmetic conditions can always be obtained by using wave-digital all-pass filters and nonrecursive FIR filters. Several design examples are included illustrating the properties of the new filters