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Positive Trigonometric Polynomials and Signal Processing Applications
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Positive and sum-of-squares polynomials have received a special interest in the latest decade, due to their connections with semidefinite programming. Thus, efficient optimization methods can be employed to solve diverse problems involving polynomials. This book gathers the main recent results on positive trigonometric polynomials within a unitary framework; the theoretical results are obtained partly from the general theory of real polynomials, partly from self-sustained developments. The optimization applications cover a field different from that of real polynomials, mainly in signal processing problems: design of 1-D and 2-D FIR or IIR filters, design of orthogonal filterbanks and wavelets, stability of multidimensional discrete-time systems. "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.
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Subject categories
- Academic > Mathematics > Algebra > Inequalities (Mathematics)
- Academic > Mathematics > Algebra > Polynomials
- Academic > Mathematics > General > Vinogradov, Ivan Matveevich, 1891-
- Academic > Mathematics > General > Mathematics; Periodicals
- Academic > Mathematics > General > Mathematics; Study and teaching
- Mathematics > Calculus
- Mathematics > Trigonometry
ISBNs
1402051255
9781402051241
9781402051258