报告人：杨在（西安交通大学）

报告题目：The Carathéodory-Fejér Theorem for Toeplitz Covariance Matrices and Spectral Analysis of Signals

报告摘要：Spectral analysis of signals is aimed at finding their frequency information from limited temporal/spatial samples and is a core component of modern information techniques. The rapid developments of radar detection and wireless communications have advanced its research from fast Fourier transform (FFT) in the 1960s to subspace methods emerging in the 1970s, and then to sparse and compressed sensing methods of this century. In this talk, we revisit the Carathéodory-Fejér Theorem (1911) on Vandermonde decomposition of Toeplitz covariance matrices and discuss its key role in spectral analysis of the past half century. We emphasize our extension of the Carathéodory-Fejér Theorem from 1-D to high dimensions and show how it forms the basis of previous approaches and innovates novel maximum likelihood methods for spectral analysis.

报告时间：2025年4月24日（星期四）16:00-17:30

报告地点：东32楼102会议室

邀请人：刘海霞

报告人简介：杨在，西安交通大学教授、博士生导师，国家优秀青年基金获得者，西交-华为数学技术联合实验室副主任。2007和2009年分获中山大学应用数学本科和硕士学位，2014年获新加坡南洋理工大学博士学位。主要从事信号处理的基础理论与方法研究，解决了Carathéodory-Fejér定理高维形式、两奇异半正定矩阵Hadamard积的正定性判定等公开问题，在IEEE Trans. Inf. Theory、IEEE Trans. Signal Process.、Appl. Comput. Harmonic Anal.、SIAM等期刊与会议发表学术论文70余篇，谷歌学术引用4300余次。现任IEEE Trans. Signal Process.和(Elsevier) Signal Processing期刊编委，IEEE信号处理学会传感器阵列与多通道（SAM）技术委员会委员，曾任欧洲信号处理会议Tutorial授课人等。主持或完成国家基金委优青、面上及青年基金，科技部重点研发课题，以及多项华为企业横向课题等。以第一完成人获陕西高等学校科学技术研究优秀成果特等奖。