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

Abstract

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 which implies that the maximal sample frequency for the overall filter is 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.

Optimal design of IIR frequency-response-masking filters using second-order cone programming

“…T HE frequency-response-masking (FRM) technique proposed by Lim [1] has proven effectiveness for the design of digital filters with narrow transition bands that can be implemented with reduced complexity compared to other options [2]- [10]. As illustrated in Fig.…”

“…In [10], a method for the design of recursive FRM filters with two allpass filters (called model filters) replacing the prototype filter and the delay line is proposed. The design in [10] is accomplished using a two-stage approach in that a good initial point is obtained by separately optimizing the model filters and the masking filters, and then a second-stage optimization is carried out to finalize the design.…”

“…The design in [10] is accomplished using a two-stage approach in that a good initial point is obtained by separately optimizing the model filters and the masking filters, and then a second-stage optimization is carried out to finalize the design. Multistage recursive FRM filters were not considered.…”

A semi-definite programming (SDP) method for designing IIR sharp cut-off digital filters using frequency-response masking

“…This is because their z variables are upsampled by a factor of M to achieve a very narrow transition band. Although the allpassbased model filter approach considered in [7] helps to reduce somewhat the system delay, the delay and stopband attenuation of an allpass-based (AP) filter are still tied up by the order of the AP filters. That is, for a given stopband attenuation, the order and hence the system delay of the filter are fixed.…”

“…To further reduce the system delay of FRM filters, low-delay (LD) FIR subfilters were proposed to realize the model and masking filters in the FRM structure [4][5][6]. FRM filters employing an allpass-based (AP) IIR model filter and a linear-phase FIR masking filters were recently proposed in [7]. The model and masking filters are first designed separately and nonlinear optimization is then applied to search for the optimal solution.…”