Positive Trigonometric Polynomials and Signal Processing Applications

  • Bogdan Dumitrescu

Part of the Signals and Communication Technology book series (SCT)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Bogdan Dumitrescu
    Pages 1-21
  3. Bogdan Dumitrescu
    Pages 23-69
  4. Bogdan Dumitrescu
    Pages 71-121
  5. Bogdan Dumitrescu
    Pages 123-147
  6. Bogdan Dumitrescu
    Pages 149-177
  7. Bogdan Dumitrescu
    Pages 179-203
  8. Bogdan Dumitrescu
    Pages 205-225
  9. Bogdan Dumitrescu
    Pages 227-242
  10. Bogdan Dumitrescu
    Pages 243-262
  11. Back Matter
    Pages 263-276

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 books 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.
  • 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.


Interpolation Positive trigonometric polynomials algorithms filter design multidimensional systems optimization semidefinite programming sum-of-squares polynomials Signal processing

Authors and affiliations

  • Bogdan Dumitrescu
    • 1
  1. 1.Department of Automatic Control and ComputersUniversity Politehnica of BucharestBucharestRomania

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-53687-3
  • Online ISBN 978-3-319-53688-0
  • Series Print ISSN 1860-4862
  • Series Online ISSN 1860-4870
  • Buy this book on publisher's site