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Produktbild: Dumitrescu, B: Positive Trigonometric Polynomials and Signal
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Dumitrescu, B: Positive Trigonometric Polynomials and Signal

Aus der Reihe Signals and Communication Technology
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139,99 € UVP 160,49 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Verlag

Springer Netherland

Seitenzahl

242

Maße (L/B/H)

1,3/15,6/23,4 cm

Sprache

Englisch

ISBN

978-90-481-7288-7

Beschreibung

Rezension

From the reviews:

"The book under review is a new contribution on the topic, with a focus on signal processing applications. ... this is the first self-contained manuscript on this emerging research area, and hence it is a welcome and timely contribution to the technical literature. ... use of illustrative numerical examples, accompanied by Matlab scripts, allows the inexperienced reader to grasp the essential ideas without having to understand all the mathematical subtelties. In particular, signal processing engineers should benefit a lot from reading the book ... ." (Didier Henrion, Zentralblatt MATH, Vol. 1126 (3), 2008)

"Trigonometric polynomials that are positive on the unit circle play an essential role in a number of digital filtering problems. ... The text would be quite suitable for use as the basis of lectures, for it has proofs written out, a survey of the literature and many exercises." (A. Bultheel, Mathematical Reviews, Issue 2007 m)

Produktdetails

Einband

Taschenbuch

Verlag

Springer Netherland

Seitenzahl

242

Maße (L/B/H)

1,3/15,6/23,4 cm

Sprache

Englisch

ISBN

978-90-481-7288-7

Herstelleradresse

Springer Netherlands
Haberstr. 7
69126 Heidelberg
DE
buchhandel-buch@springer.com

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  • Produktbild: Dumitrescu, B: Positive Trigonometric Polynomials and Signal
  • 1. Positive polynomials. 1.1 Types of polynomials. 1.2 Positive polynomials. 1.3 Toeplitz positivity conditions. 1.4 Positivity on an interval. 1.5 Details and other facts. 1.6 Bibliographical and historical notes. 2. Gram matrix representation. 2.1 Parameterization of trigonometric polynomials. 2.2 Optimization using the trace parameterization. 2.3 Toeplitz quadratic optimization. 2.4 Duality. 2.5 Kalman-Yakubovich-Popov lemma. 2.6 Spectral factorization from a Gram matrix. 2.7 Parameterization of real polynomials. 2.8 Choosing the right basis. 2.9 Interpolation representations. 2.10 Mixed representations. 2.11 Fast algorithms. 2.12 Details and other facts. 2.13 Bibliographical and historical notes. 3. Multivariate polynomials. 3.1 Multivariate polynomials. 3.2 Sum-of-squares multivariate polynomials. 3.3 Sum-of-squares of real polynomials. 3.4 Gram matrices of trigonometric polynomials. 3.5 Sum-of-squares relaxations. 3.6 Gram matrices from partial bases. 3.7 Gram matrices of real multivariate polynomials. 3.8 Pairs of relaxations. 3.9 The Gram pair parameterization. 3.10 Polynomials with matrix coefficients. 3.11 Details and other facts. 3.12 Bibliographical and historical notes. 4. Polynomials positive on domains. 4.1 Real polynomials positive on compact domains. 4.2 Polynomials positive on frequency domains. 4.3 Bounded Real Lemma. 4.4 Positivstellensatz. 4.5 Details and other facts. 4.6 Bibliographical and historical notes. 5. Design of FIR filters. 5.1 Design of FIR filters. 5.2 Design of 2-D FIR filters. 5.3 FIR deconvolution. 5.4 Bibliographical and historical notes. 6. Orthogonal filterbanks. 6.1 Two-channel filterbanks. 6.2 Signal-adapted wavelets. 6.3 GDFT modulated filterbanks. 6.4 Bibliographical and historical notes. 7. Stability. 7.1 Multidimensional stability tests. 7.2 Robust stability. 7.3 Convex stability domains. 7.4 Bibliographical and historical notes. 8. Design of IIR filters. 8.1 Magnitude design of IIR filters. 8.2 Approximate linear-phase designs. 8.3 2D IIR filter design. 8.4 Bibliographical and historical notes Appendix A: semidefinite programming. Appendix B: spectral factorization. References.