Positive Trigonometric Polynomials and Signal Processing Applications
暫譯: 正三角多項式與信號處理應用
Dumitrescu, Bogdan
- 出版商: Springer
- 出版日期: 2018-07-21
- 售價: $4,600
- 貴賓價: 9.5 折 $4,370
- 語言: 英文
- 頁數: 276
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3319852175
- ISBN-13: 9783319852171
海外代購書籍(需單獨結帳)
商品描述
Positive and sum-of-squares polynomials have received a special interest in the latest decade, due to their connections with semidefinite programming. Thus, efficient optimization methods can be employed to solve diverse problems involving polynomials. This book gathers the main recent results on positive trigonometric polynomials within a unitary framework; the theoretical results are obtained partly from the general theory of real polynomials, partly from self-sustained developments. The optimization applications cover a field different from that of real polynomials, mainly in signal processing problems: design of 1-D and 2-D FIR or IIR filters, design of orthogonal filterbanks and wavelets, stability of multidimensional discrete-time systems.
Positive Trigonometric Polynomials and Signal Processing Applications has two parts: theory and applications. The theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The presentation starts by giving the main results for univariate polynomials, which are later extended and generalized for multivariate polynomials. The applications part is organized as a collection of related problems that use systematically the theoretical results. All the problems are brought to a semidefinite programming form, ready to be solved with algorithms freely available, like those from the library SeDuMi.
商品描述(中文翻譯)
正的和平方和多項式在最近十年受到特別關注，因為它們與半正定規劃的關聯。因此，可以採用有效的優化方法來解決涉及多項式的各種問題。本書匯集了在單位框架內有關正三角多項式的主要最新結果；這些理論結果部分來自實數多項式的一般理論，部分來自自我持續的發展。優化應用涵蓋了與實數多項式不同的領域，主要集中在信號處理問題上：設計一維和二維的FIR或IIR濾波器、設計正交濾波器組和小波、以及多維離散時間系統的穩定性。
《正的三角多項式及其信號處理應用》分為兩個部分：理論和應用。平方和三角多項式的理論基於Gram矩陣的概念（擴展到Gram對或Gram集合）進行統一呈現。介紹首先給出單變量多項式的主要結果，然後擴展和概括到多變量多項式。應用部分則組織為一系列相關問題，系統性地使用理論結果。所有問題都轉化為半正定規劃形式，準備使用可自由獲得的算法進行求解，例如來自SeDuMi庫的算法。
作者簡介
Bogdan Dumitrescu received his M.S. and Ph.D. from University Politehnica of Bucharest, Romania. He is a Professor with the Department of Automatic Control and Computers, University Politehnica of Bucharest. He held several visiting research positions at Tampere International Center for Signal Processing, Tampere University of Technology, Finland, in particular that of FiDiPro fellow (2010-2013). He was Associate Editor (2008-2012) and Area Editor (2010-2014) at IEEE Transactions on Signal Processing. He is the author of the book "Positive trigonometric polynomials and signal processing applications." His scientific interests are in optimization, numerical methods, and their applications to signal processing.
作者簡介(中文翻譯)
博格丹·杜米特雷斯庫（Bogdan Dumitrescu）於羅馬尼亞布加勒斯特理工大學（University Politehnica of Bucharest）獲得碩士和博士學位。他是布加勒斯特理工大學自動控制與計算機系的教授。他曾在芬蘭坦佩雷科技大學（Tampere University of Technology）的坦佩雷國際信號處理中心（Tampere International Center for Signal Processing）擔任多個訪問研究職位，特別是擔任FiDiPro研究員（2010-2013）。他曾擔任《IEEE信號處理學報》（IEEE Transactions on Signal Processing）的副編輯（2008-2012）和區域編輯（2010-2014）。他是《正三角多項式及其在信號處理中的應用》（'Positive trigonometric polynomials and signal processing applications.'）一書的作者。他的科學興趣包括優化、數值方法及其在信號處理中的應用。
