03112nmm a2200445 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002300139245012100162250001700283260005600300300006200356505032200418653001700740653004000757653002400797653002800821653002600849653002100875653001300896653004700909653002400956653003000980653001301010653002701023653002501050653002201075653003001097653001301127710003401140041001901174989003601193490004101229856007201270082001201342520131201354EB001383890EBX0100000000000000090685500000000000000.0cr|||||||||||||||||||||170406 ||| eng a97833195368801 aDumitrescu, Bogdan00aPositive Trigonometric Polynomials and Signal Processing ApplicationshElektronische Ressourcecby Bogdan Dumitrescu a2nd ed. 2017 aChambSpringer International Publishingc2017, 2017 aXVI, 276 p. 51 illus., 1 illus. in colorbonline resource0 aPositive Polynomials -- Gram Matrix Representation -- Multivariate Polynomials -- Polynomials Positive on Domains -- Design of FIR Filters -- Orthogonal Filterbanks -- Stability -- Design of IIR Filters -- Optimization with the Atomic Norm -- Appendix A: Semidefinite Programming -- Appendix B: Spectral Factorization aOptimization aSignal, Image and Speech Processing aApplied mathematics aEngineering mathematics aMathematical analysis aImage processing aAnalysis aMathematical and Computational Engineering aElectronic circuits aSpeech processing systems aGeometry aAnalysis (Mathematics) aCircuits and Systems aSignal processing aMathematical optimization aGeometry2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aSignals and Communication Technology uhttps://doi.org/10.1007/978-3-319-53688-0?nosfx=yxVerlag3Volltext0 a621.382 aThis 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