EigenValue Optimization Techniques For Designing Optimum FIR Compaction Filters

Abstract

In this paper we propose a new technique for finding the optimum FIR
compaction filter adapted to signal statistics. The main novelty of our approach is
the transformation of the original problem into the maximum eigenvalue minimization of a parameterized Toeplitz matrix, with a low number of variables. This is
a typical application of semidefinite programming and may be solved with reliable
interior-point algorithms. The optimal filter is then found either solving a quadratic
system with a Newton-Raphson algorithm, or via a matrix Riccati equation. The
numerical experiments show that the optimal compaction filter is obtained with good
numerical accuracy and affordable execution time for filters of order up to 100. A
characterization of optimal filters is also given, coherent with our matrix formulation
of the optimization problem.