Reduction of Symmetric Complex Filters

Abstract

Due to their linear-phase property, symmetric filters are an interesting class of finite-impulse-response (FIR) filters. Moreover, symmetric FIR filters allow an efficient implementation. In this paper we extend the classical definition of Hermitian symmetry to a more general symmetry that is also applicable to complex filters. This symmetry is called generalized-Hermitian symmetry. We show the usefulness of this definition as it allows for a unified treatment of even and odd-length filters. Central in this paper is a theorem on the reduction of generalized-Hermitian-symmetric filters to Hermitian-symmetric filters, both with finite precision coefficients. A constructive proof of this theorem is presented and an associated procedure for reducing generalized-Hermitian-symmetric filters is derived. Two of the examples show the application of the reduction procedure and the achieved savings on arithmetic costs. Finally, all three examples show that a special instance of the generalized-Hermitian-symmetric filters with finite precision coefficients, may have lower arithmetic costs than the Hermitian-symmetric filter from which it is derived.

DOI: 10.1109/TSP.2009.2028092

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Cite this paper

@article{Bruekers2010ReductionOS, title={Reduction of Symmetric Complex Filters}, author={Fons Bruekers and Ton Kalker}, journal={IEEE Transactions on Signal Processing}, year={2010}, volume={58}, pages={200-208} }