2025/03/19 by Dehui Yang, Yang, Dehui, Xi Feng +1 · 1 citation
Chemistry · #Audio and Speech Processing (eess.AS) #FOS: Electrical engineering #Molecular spectroscopy and chirality #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2503.15164
openalex publication_date 2025/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the fundamental problem of estimating chirp parameters from a mixture of linear chirp signals. Unlike most previous methods, which solve the problem by discretizing the parameter space and then estimating the chirp parameters, we propose a gridless approach by reformulating the inverse problem as a constrained two-dimensional atomic norm minimization from structured measurements. This reformulation enables the direct estimation of continuous-valued parameters without discretization, thereby resolving the issue of basis mismatch. An approximate semidefinite programming (SDP) is employed to solve the proposed convex program. Additionally, a dual polynomial is constructed to certify the optimality of the atomic decomposition. Numerical simulations demonstrate that exact recovery of chirp parameters is achievable using the proposed atomic norm minimization.