Title:
Positive trigonometric polynomials and signal processing applications
Personal Author:
Series:
Signals and communication technology
Publication Information:
Dordrecht : Springer, 2007
ISBN:
9781402051241
General Note:
Also available online version
Electronic Access:
Full Text
DSP_RESTRICTION_NOTE:
Accessible within UTM campus
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010156687 | QA161.P59 D85 2007 | Open Access Book | Book | Searching... |
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Summary
Summary
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.
Table of Contents
| 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 |
