A Novel Systematic Approach for Synthesizing Multiplication-Free Highly-Selective FIR Half-Band Decimators and Interpolators

This paper discloses a systematic approach to generating for sampling rate applications multiplication-free linear-phase finite-impulse response half-band filters based on an article by Saramaki, Karema, Ritoniemi, and Tenhunen. This article counts on the following facts. First, the transfer function of such filters is expressible as a sum of the terms (1/2)z^-M and G(z²), where M is odd and is the order of G(z). Second, G(z) is constructed using identical copies of the same sub-filter that are properly interconnected with the aid a few additional adders and tap coefficients. The first step is to quantize in a simple manner the additional tap coefficient values to be a few powers-of-two terms. The second step is to find the sub-filter coefficient values in the same representation forms. This can be accomplished using a very simple quantization technique because the ripple values for the sub-filter are very huge compared to the overall filter. In addition, efficient structures for implementing both the resulting decimators and interpolators are given. An example in the above-mentioned article is included for illustrating the efficiency of the proposed multiplication-free structures compared with the conventional direct-form designs