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.
嘉宾介绍
杨在，西安交通大学数学与统计学院教授、博士生导师，西安交大-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。主要从事信息处理与无线通信的数学理论与方法研究，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60余篇，谷歌学术引用4000余次。任或曾任IEEE Trans. Signal Process.编委、欧洲信号处理会议Tutorial授课人、IEEE信号处理学会传感器阵列与多通道（SAM）技术委员会委员等。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。
