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In this paper we propose a new method of processing speech degraded by reverberation. The method is based on analysis of short (2 ms) segments of data to enhance the regions in the speech signal having high Signal to Reverber-ant component Ratio (SRR). The short segment analysis shows that SRR is diierent in diierent segments of speech. The processing method involves identifying and manipulatin...

3 Polynomial Optimization, Sums of Squares, and Applications 47 Pablo A. Parrilo 3.1 Nonnegative Polynomials and Sums of Squares . . . . . . . . . . 48 3.2 Applications of Sum of Squares Programs . . . . . . . . . . . . . 76 3.3 Special Cases and Structure Exploitation . . . . . . . . . . . . . 86 3.4 Infeasibility Certificates . . . . . . . . . . . . . . . . . . . . . . . 106 3.5 Duality and S...

Representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of a sum of squares optimization and SDP (semidefinite programming) relaxation of polynomial optimization problems. We disscuss effective methods to get a simpler representation of a “sparse” polynomial as a sum of squares of sparse pol...

In this paper, we extend Bai and Perron’s (1998, Econometrica, p.47-78) framework for multiple break testing to linear models estimated via Two Stage Least Squares (2SLS). Within our framework, the break points are estimated simultaneously with the regression parameters via minimization of the residual sum of squares on the second step of the 2SLS estimation. We establish the consistency of the...

Abstract We prove decomposition theorems for sparse positive (semi)definite polynomial matrices that can be viewed as sparsity-exploiting versions of the Hilbert–Artin, Reznick, Putinar, and Putinar–Vasilescu Positivstellensätze. First, we establish a matrix P ( x ) with chordal sparsity is semidefinite all $$x\in \mathbb {R}^n$$ <mml:mr...

SOSTOOLS is a MATLAB toolbox for constructing and solving sum of squares programs. It can be used in combination with semidefinite programming software, such as SeDuMi, to solve many continuous and combinatorial optimization problems, as well as various control-related problems. This paper provides an overview on sum of squares programming, describes the primary features of SOSTOOLS, and shows ...