This document proposes a two-step tree search algorithm for designing multiplierless linear phase FIR filters to reduce design time. The first step uses a polynomial-time search where each coefficient is fixed to a single discrete value. The second step keeps small coefficients from the first step fixed while further optimizing large coefficients by dividing them into groups and optimizing each group alternately. This two-step approach aims to maximize computational resources and achieve lower hardware cost designs in less time than existing algorithms.

1. TWO-STEP OPTIMIZATION APPROACH FOR THE DESIGN OF
MULTIPLIERLESS LINEAR-PHASE FIR FILTERS
ABSTRACT:
Deterministic tree search algorithms for the design of multiplierless linear phase finite
impulse response filters are generally time consuming. Many researches therefore focus on how
to restrict the number of discrete values assigned to each coefficient during a tree search. In this
paper, a two-step tree search algorithm is proposed. In the first step, a polynomial-time tree
search algorithm where each coefficient is fixed to a single one discrete value is introduced.
Since the synthesis of large coefficients is dominant in the hardware cost over small coefficients,
in the second step optimization, the small coefficients obtained in the first step is kept unaltered
and the large coefficients are further divided into several groups and the coefficients are
optimized group by group alternatingly. Such a two-step search strategy maximally utilizes the
limited computational resources and can achieve lower hardware cost design in a shorter design
time, compared with existing algorithms.