Revisit of the Eigenfilter Method for the Design of FIR Filters and Wideband Beamformers

TL;DR

This paper critically revisits the eigenfilter method for FIR filter and wideband beamformer design, identifying a key performance issue and proposing a constraint-based solution to improve response accuracy.

Contribution

It reveals a formulation problem in the eigenfilter method and introduces an additional constraint to enhance filter and beamformer performance.

Findings

Identified a performance issue in passband and mainlobe responses.

Proposed a constraint to mitigate the performance issue.

Demonstrated improved design examples with the proposed method.

Abstract

The least squares based eigenfilter method has been applied to the design of both finite impulse response (FIR) filters and wideband beamformers successfully. It involves calculating the resultant filter coefficients as the eigenvector of an appropriate Hermitian matrix, and offers lower complexity and less computation time with better numerical stability as compared to the standard least squares method. In this paper, we revisit the method and critically analyze the eigenfilter method by revealing a serious performance issue in the passband of the designed FIR filter and the mainlobe of the wideband beamformer, which occurs due to a formulation problem. A solution is then proposed to mitigate this issue by imposing an additional constraint to control the response at the passband/mainlode, and design examples for both FIR filters and wideband beamformers are provided to demonstrate the effectiveness of the proposed method.