7,742 research outputs found
Time and spectral domain relative entropy: A new approach to multivariate spectral estimation
The concept of spectral relative entropy rate is introduced for jointly
stationary Gaussian processes. Using classical information-theoretic results,
we establish a remarkable connection between time and spectral domain relative
entropy rates. This naturally leads to a new spectral estimation technique
where a multivariate version of the Itakura-Saito distance is employed}. It may
be viewed as an extension of the approach, called THREE, introduced by Byrnes,
Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the
Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the
form of a constrained spectrum approximation problem where the distance is
equal to the processes relative entropy rate. The corresponding solution
entails a complexity upper bound which improves on the one so far available in
the multichannel framework. Indeed, it is equal to the one featured by THREE in
the scalar case. The solution is computed via a globally convergent matricial
Newton-type algorithm. Simulations suggest the effectiveness of the new
technique in tackling multivariate spectral estimation tasks, especially in the
case of short data records.Comment: 32 pages, submitted for publicatio
Trapped Modes in Linear Quantum Stochastic Networks with Delays
Networks of open quantum systems with feedback have become an active area of
research for applications such as quantum control, quantum communication and
coherent information processing. A canonical formalism for the interconnection
of open quantum systems using quantum stochastic differential equations (QSDEs)
has been developed by Gough, James and co-workers and has been used to develop
practical modeling approaches for complex quantum optical, microwave and
optomechanical circuits/networks. In this paper we fill a significant gap in
existing methodology by showing how trapped modes resulting from feedback via
coupled channels with finite propagation delays can be identified
systematically in a given passive linear network. Our method is based on the
Blaschke-Potapov multiplicative factorization theorem for inner matrix-valued
functions, which has been applied in the past to analog electronic networks.
Our results provide a basis for extending the Quantum Hardware Description
Language (QHDL) framework for automated quantum network model construction
(Tezak \textit{et al.} in Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci.
370(1979):5270-5290, to efficiently treat scenarios in which each
interconnection of components has an associated signal propagation time delay
Asymptotic Uniqueness of Best Rational Approximants to Complex Cauchy Transforms in of the Circle
For all n large enough, we show uniqueness of a critical point in best
rational approximation of degree n, in the L^2-sense on the unit circle, to
functions f, where f is a sum of a Cauchy transform of a complex measure \mu
supported on a real interval included in (-1,1), whose Radon-Nikodym derivative
with respect to the arcsine distribution on its support is Dini-continuous,
non-vanishing and with and argument of bounded variation, and of a rational
function with no poles on the support of \mu.Comment: 28 page
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