On minimum phase transformation and filter design

TL;DR

This paper clarifies the theoretical principles behind minimum-phase filter design, especially for Chebyshev filters, and demonstrates how applying these principles improves filter accuracy and convergence in design algorithms.

Contribution

It reveals a mismatch between practice and theory in Chebyshev minimum-phase filter design and proposes a revised factorization approach for better accuracy and convergence.

Findings

Revised factorization improves filter tap accuracy

Initial values lead to faster convergence in design algorithms

Numerical results confirm theoretical improvements

Abstract

Minimum-phase finite impulse response filters are widely used in practice, and much research has been devoted to the design of such filters. However, for the important case of Chebyshev filters there is a curious mismatch between current best practice and well-established theoretical principles. The paper shows that this difference can be understood through analysis of the time-domain factorization of a suitable extended matrix. This analysis explains why the definition of a factorable linear phase filter must be revised. The time domain analysis of factorization suggests initial values leading to fast and accurate convergence of iterative algorithms for the design of minimum-phase finite impulse response filters. Numerical results are provided to demonstrate that a significant improvement in filter tap accuracy is obtained when the well-established theoretical principles are correctly applied to the design of minimum phase finite impulse response filters.