A fast alternating projection method for complex frequency estimation

TL;DR

This paper introduces a rapid alternating projection technique for complex frequency estimation, providing theoretical convergence guarantees and demonstrating improved performance over traditional methods like MUSIC and ESPRIT.

Contribution

The paper presents a novel fast alternating projection algorithm for complex frequency estimation with proven convergence and error bounds, outperforming existing methods.

Findings

The proposed method converges reliably with proven rates.

Numerical results show improved accuracy over MUSIC and ESPRIT.

Fast algorithms are developed for practical implementation.

Abstract

The problem of approximating a sampled function using sums of a fixed number of complex exponentials is considered. We use alternating projections between fixed rank matrices and Hankel matrices to obtain such an approximation. Convergence, convergence rates and error estimates for this technique are proven, and fast algorithms are developed. We compare the numerical results obtain with the MUSIC and ESPRIT methods.