Overview
- Features updated information on LMI parameterizations of sum-of-squares trigonometric polynomials
- Contains applications in optimization of 1-D and 2-D filter design, orthogonal filterbanks
- Includes a new chapter dedicated to applications in super-resolution theory that connects to a currently very active research area
- Includes supplementary material: sn.pub/extras
Part of the book series: Signals and Communication Technology (SCT)
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Table of contents (9 chapters)
Keywords
About this book
This revised edition is made up of two parts: theory and applications. Though many of the fundamental results are still valid and used, new and revised material is woven throughout the text. As with the original book, 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 programming environment has also evolved, and the book’s examples are changed accordingly. The applications section is organized as a collection of related problems that use systematically the theoretical results. All the problems are brought to a semi-definite programming form, ready to be solved with algorithms freely available, like those from the libraries SeDuMi, CVX and Pos3Poly. A new chapter discusses applications in super-resolution theory, where Bounded Real Lemma for trigonometric polynomials is an important tool. This revision is written to be more appealing and easier to use for new readers.
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Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Positive Trigonometric Polynomials and Signal Processing Applications
Authors: Bogdan Dumitrescu
Series Title: Signals and Communication Technology
DOI: https://doi.org/10.1007/978-3-319-53688-0
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2017
Hardcover ISBN: 978-3-319-53687-3Published: 27 March 2017
Softcover ISBN: 978-3-319-85217-1Published: 21 July 2018
eBook ISBN: 978-3-319-53688-0Published: 20 March 2017
Series ISSN: 1860-4862
Series E-ISSN: 1860-4870
Edition Number: 2
Number of Pages: XVI, 276
Number of Illustrations: 50 b/w illustrations, 1 illustrations in colour
Topics: Signal, Image and Speech Processing, Mathematical and Computational Engineering, Circuits and Systems, Analysis, Geometry, Optimization