Extrapolated impulse response filter and its application in the synthesis of digital filters using the frequency-response masking technique

Abstract

Techniques based on the frequency-response masking (FRM) approach are known to be highly effective for reducing the number of multipliers and adders in linear-phase finite-impulse response (FIR) filters. The basic FRM structure comprises a band-edge shaping filter and two masking filters. It is observed that the impulse response of the band-edge shaping filter of an FRM structure exhibits a quasi-periodic property. Previous study showed that lowpass or highpass digital FIR filters, whose impulse responses are quasi-periodic, can be synthesized using extrapolated impulse response technique, which leads to structure with much reduced arithmetic complexity. In this paper, an implementation of the extrapolated impulse response filter is presented. An FRM technique incorporating extrapolated impulse response band-edge shaping filter is introduced. An iterative optimization procedure is proposed to design the FRM sub-filters. It is demonstrated using an example taken from the literature that our new technique produces a saving of over 20% in the number of multipliers used.