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In this paper, a novel optimization technique is proposed to optimize filter coefficients of linear phase finite-impulse response (FIR) filter to share common subexpressions within and among coefficients. Existing approaches of common subexpression elimination optimize digital filters in two stages: first, an FIR filter is designed in a discrete space such as finite wordlength space or signed power-of-two (SPT) space to meet a given specification; in the second stage, an optimization algorithm is applied on the discrete coefficients to find and eliminate the common subexpressions. Such a two-stage optimization technique suffers from the problem that the search space in the second stage is limited by the finite wordlength or SPT coefficients obtained in the first stage optimization. The new proposed algorithm overcomes this problem by optimizing the filter coefficients directly in subexpression space for a given specification. Numerical examples of benchmark filters show that the required number of adders obtained using the proposed algorithm is much less than those obtained using two-stage optimization approaches.

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.

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