Design of Linear Phase FIR Filters in Subexpression Space Using Mixed Integer Linear Programming

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:...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. 1, Fundamental theory and applications Fundamental theory and applications, 2007-10, Vol.54 (10), p.2330-2338
Main Authors: Yu, Ya Jun, Lim, Yong Ching
Format: Article
Language:English
Subjects:
Adders
Algorithm design and analysis
Algorithms
Common subexpression sharing
Design optimization
Digital filters
Finite impulse response filter
finite-impulse response (FIR) filters
FIR filters
IIR filters
Limit-cycles
Linear phase
Mathematical analysis
Mathematical models
Mixed integer linear programming
mixed integer linear programming (MILP)
Nonlinear filters
Optimization
Optimization techniques
Specifications
Stability
Studies
subexpression space
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Summary: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.
ISSN:1549-8328
1057-7122
1558-0806
DOI:10.1109/TCSI.2007.904599