Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal analytic properties of noise. Introducing the J-Matrix
  formalism   We propose a new method in the spectral analysis of noisy time-series data
for damped oscillators. From the Jacobi three terms recursive relation for the
denominators of the Pad\'e Approximations built on the well-known Z-transform
of an infinite time-series, we build an Hilbert space operator, a J-Operator,
where each bound state (inside the unit circle in the complex plane) is simply
associated to one damped oscillator while the continuous spectrum of the
J-Operator, which lies on the unit circle itself, is shown to represent the
noise. Signal and noise are thus clearly separated in the complex plane. For a
finite time series of length 2N, the J-operator is replaced by a finite order
J-Matrix J_N, having N eigenvalues which are time reversal covariant. Different
classes of input noise, such as blank (white and uniform), Gaussian and pink,
are discussed in detail, the J-Matrix formalism allowing us to efficiently
calculate hundreds of poles of the Z-transform. Evidence of a universal
behaviour in the final statistical distribution of the associated poles and
zeros of the Z-transform is shown. In particular the poles and zeros tend, when
the length of the time series goes to infinity, to a uniform angular
distribution on the unit circle. Therefore at finite order, the roots of unity
in the complex plane appear to be noise attractors. We show that the
Z-transform presents the exceptional feature of allowing lossless undersampling
and how to make use of this property. A few basic examples are given to suggest
the power of the proposed method.

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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph