Optimization of Linear Phase FIR Filters in Dynamically Expanding Subexpression Space

Abstract

The most advanced techniques in the design of multiplierless finite impulse response (FIR) filters explore common subexpression sharing when the filter coefficients are optimized. Existing techniques, however, either suffer from a heavy computational overhead, or have no guarantees on the minimal hardware cost in terms of the number of adders. A recent technique capable of designing long filters optimizes filter coefficients in pre-specified subexpression spaces. The pre-specified subexpression spaces determine if a filter with fewer adders may be achieved. Unfortunately, there is no known technique that can find subexpression spaces that can guarantee the solution with the minimum number of adders in the implementation. In this paper, a tree search algorithm is proposed to update and expand the subexpression spaces dynamically, and thus, to achieve the maximum subexpression sharing during the optimization. Numerical examples show that the proposed algorithm generates filters using fewer adders than other non-optimum algorithms. On the other hand, as a consequence of its efficiency, our proposed technique is able to design longer filters than the global optimum algorithm.

Exact and Approximate Algorithms for the Filter Design Optimization Problem

“…Thus, a scaling factor can be added into the filter constraints as a continuous variable as follows [25], [26]: (4) where and are respectively the lower and upper bounds of . Furthermore, in some DSP applications, it is desirable to minimize the peak weighted ripple [18], the normalized peak ripple (NPR) [28], [29], or the NPR magnitude [27].…”

“…Since there exist many possible sets of coefficients satisfying the filter constraints, FDO algorithms incorporate sophisticated techniques such as local search [18], [24], [27] and exhaustive search methods, including branch-and-bound [22], [23], [25], DFS [28], [29], and MILP [17], [19], [21], [24], [26] techniques. The local search methods can be applied to filters with a large number of coefficients, but the optimal solution cannot be ensured, since the entire search space is not explored.…”

Analysis of Various MCM Algorithms for Reconfigurable RRC Fir Filter

“…The Common Subexpression Elimination (CSE) [4][5] deals with the elimination of common subexpressions within the coefficients. The Common subexpressions are equivalent to the common digit patterns.…”

High Performance Reconfigurable FIR Filter Architecture Using Optimized Multiplier

“…A combiner is used to detect the earliest transition between the two paths and latch the result for transfer to the next stage. Proper skewing is achieved by preferential sizing of the pull-up and pulldown transistors in static CMOS circuits [5,14,20]. CSA using DTSL is shown in Fig.…”