Positive Trigonometric Polynomials and Signal Processing Applications - Dumitrescu, Bogdan; SpringerLink (Online service) (Dordrecht : Springer Netherlands, 2007)
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.
POSITIVE POLYNOMIALS -- GRAM MATRIX REPRESENTATION -- MULTIVARIATE POLYNOMIALS -- POLYNOMIALS POSITIVE ON DOMAINS -- DESIGN OF FIR FILTERS -- ORTHOGONAL FILTERBANKS -- STABILITY -- DESIGN OF IIR FILTERS.
Keywords: Mathematics; Mathematical analysis; Analysis (Mathematics).; Geometry; Mathematical optimization; Applied mathematics; Engineering mathematics; Electronic circuits; Mathematics; Analysis; Geometry; Signal, Image and Speech Processing; Appl.Mathematics/Computational Methods of Engineering; Optimization; Circuits and Systems; Electronic books