Symbolic optimization of algebraic functions
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Solution of algebraic riccati equations using the sum of roots
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Optimized analog filter designs with flat responses by semidefinite programming
IEEE Transactions on Signal Processing
Tight wavelet frames via semi-definite programming
Journal of Approximation Theory
Fir smoothing of discrete-time polynomial signals in state space
IEEE Transactions on Signal Processing
Minimax design of IIR digital filters using iterative SOCP
IEEE Transactions on Circuits and Systems Part I: Regular Papers
A Doppler robust max-min approach to radar code design
IEEE Transactions on Signal Processing
Design of optimal controllers for spatially invariant systems with finite communication speed
Automatica (Journal of IFAC)
Brief paper: A hierarchy of LMI inner approximations of the set of stable polynomials
Automatica (Journal of IFAC)
Smoothing of ultrasound images with the p-lag FIR structures
TELE-INFO'11/MINO'11/SIP'11 Proceedings of the 10th WSEAS international conference on Telecommunications and informatics and microelectronics, nanoelectronics, optoelectronics, and WSEAS international conference on Signal processing
Positive trigonometric polynomials for strong stability of difference equations
Automatica (Journal of IFAC)
An Exact Duality Theory for Semidefinite Programming Based on Sums of Squares
Mathematics of Operations Research
Parametrized model reduction based on semidefinite programming
Automatica (Journal of IFAC)
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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 Applicationshas 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.