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FIR filter design via spectral factorization and convex optimization
Finite impulse response filter filter coefficient variables spectral decomposition linear and nonlinear convex programming
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2015/8/11
We consider the design of finite impulse response (FIR) filters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems, with the filter coefficient...
Structural Analysis of Laplacian Spectral Properties with Application to Electric Transmission Networks
Laplacian Spectral Properties Electric Transmission Networks Optimization and Control
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2011/9/22
Abstract: The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power networks to d...
On a Devil's staircase associated to the joint spectral radii of a family of pairs of matrices
Joint spectral radius Devil’s staircase finiteness conjecture Sturmian sequence balanced word
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2011/9/14
Abstract: The joint spectral radius of a finite set of real d x d matrices is defined to be the maximum possible exponential rate of growth of products of matrices drawn from that set. In previous wor...
Distances and Riemannian metrics for multivariate spectral densities
Riemannian metrics multivariate spectral densities Optimization and Control
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2011/8/26
Abstract: We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal predic...
A Gel'fand-type spectral radius formula and stability of linear constrained switching systems
Joint/generalized spectral radius Gel’fand-type spectral-radius formula linear switched system asymptotic stability
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2011/8/22
Abstract: Using ergodic theory, in this paper we present a Gel'fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix mu...
Spectral Optimization Problems
optimization problems for eigenvalues shape optimization capacity
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2011/2/21
In this survey paper we present a class of shape optimization problems where the cost function involves the solution of a PDE of elliptic type in the unknown domain.In particular, we consider cost fun...
Spectral degeneracy and escape dynamics for intermittent maps with a hole
Escape rate Pomeau-Manneville maps Perron-Frobenius operators
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2011/1/20
We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets.
Continuity of spectral averaging
Continuity spectral averaging
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2010/12/8
We consider averages of spectral measures of rank one perturba-tions with respect to a -finite measure . It is examined how various degrees of continuity of with respect to -dimensional Hausdor...
Spectral triples and Gibbs measures for expanding maps on Cantor sets
spectral triple Dixmier trace expanding map Gibbs measure
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2010/12/14
Let T : ! be an expanding map on a Cantor set. For each suitably normalized H¨older continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as ...
A Spectral Approach to Consecutive Pattern-Avoiding Permutations
Spectral Approach Consecutive Pattern-Avoiding Permutations
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2010/12/3
We consider the problem of enumerating permutations in the symmetric group on n elements
which avoid a given set of consecutive pattern S, and in particular computing asymptotics as n
tends to infin...