Positive Trigonometric Polynomials and Signal Processing Applications

✍ Scribed by Bogdan Dumitrescu

• Publisher: Springer International Publishing AG
• Year: 2017
• Tongue: English
• Leaves: 282
• Series: Signals and Communication Technology
• Edition: Second
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Positive Polynomials....Pages 1-21
Gram Matrix Representation....Pages 23-69
Multivariate Polynomials....Pages 71-121
Polynomials Positive on Domains....Pages 123-147
Design of FIR Filters....Pages 149-177
Orthogonal Filterbanks....Pages 179-203
Stability....Pages 205-225
Design of IIR Filters....Pages 227-242
Optimization with the Atomic Norm....Pages 243-262
Back Matter....Pages 263-276