Description
This book gathers the main recent results on positive trigonometric polynomials within a unitary framework. The book 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 applications part is organized as a collection of related problems that use systematically the theoretical results. Bogdan Dumitrescu received his M.S. and Ph.D. from University Politehnica of Bucharest, Romania. He is a Professor with the Department of Automatic Control and Computers, University Politehnica of Bucharest. He held several visiting research positions at Tampere International Center for Signal Processing, Tampere University of Technology, Finland, in particular that of FiDiPro fellow (2010-2013). He was Associate Editor (2008-2012) and Area Editor (2010-2014) at IEEE Transactions on Signal Processing. He is the author of the book “Positive trigonometric polynomials and signal processing applications”. His scientific interests are in optimization, numerical methods, and their applications to signal processing. Positive 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.
