主講人：楊在

主講人簡介：楊在，西安交通大學數學與統計學院教授、博士生導師、國家優青。2007和2009年分獲中山大學應用數學本科和碩士學位，2014年獲新加坡南洋理工大學博士學位。主要從事信息處理與無線通信的數學理論與方法研究，在IEEE Trans. Inf. Theory、IEEE Trans. Signal Process.、Appl. Comput. Harmonic Anal.等期刊與會議發表學術論文60余篇，谷歌學術引用3600余次。任或曾任IEEE Trans. Signal Process.期刊編委、(Elsevier) Signal Process.期刊編委、歐洲信號處理會議Tutorial授課人、IEEE信號處理學會傳感器陣列與多通道（SAM）技術委員會委員。主持4項國家基金委項目（青年、兩個面上及優青項目）、1項科技部重點研發課題，及多項華為企業橫向課題。

報告內容概要：Spectral analysis of signals 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 modern spectral analysis. 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 methods for spectral analysis.