Add-Equalize Structures for Linear-Phase Nyquist FIR Filter Interpolators and Decimators

Abstract

This paper introduces add-equalize structures for the implementation of linear-phase Nyquist ( $M$ th-band) finite-length impulse response (FIR) filter interpolators and decimators. The paper also introduces a systematic design technique for these structures based on iteratively reweighted $\ell _{1}$ -norm minimization. In the proposed structures, the polyphase components share common parts which leads to a considerably lower implementation complexity as compared to conventional single-stage converter structures. The complexity is comparable to that of multi-stage Nyquist structures. A main advantage of the proposed structures is that they work equally well for all integer conversion factors, thus including prime numbers which cannot be handled by the regular multi-stage Nyquist converters. Moreover, the paper shows how to utilize the frequency-response masking approach to further reduce the complexity for sharp-transition specifications. It also shows how the proposed structures can be used to reduce the complexity for reconfigurable sampling rate converters. Several design examples are included to demonstrate the effectiveness of the proposed structures.