2005
DOI: 10.1016/j.jat.2004.10.014
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On the distribution of poles of Padé approximants to the Z-transform of complex Gaussian white noise

Abstract: In the application of Padé methods to signal processing a basic problem is to take into account the effect of measurement noise on the computed approximants. Qualitative deterministic noise models have been proposed which are consistent with experimental results. In this paper the Padé approximants to the Z-transform of a complex Gaussian discrete white noise process are considered. Properties of the condensed density of the Padé poles such as circular symmetry, asymptotic concentration on the unit circle and … Show more

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Cited by 26 publications
(53 citation statements)
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“…Moreover, when s 0 = s 1 = 0 we have h 2 (z, σ ) = 1 π(1+|z| 2 ) 2 which is independent of σ 2 , confirming the result obtained in [3] for the pure noise case.…”
Section: By Identifyingsupporting
confidence: 86%
See 2 more Smart Citations
“…Moreover, when s 0 = s 1 = 0 we have h 2 (z, σ ) = 1 π(1+|z| 2 ) 2 which is independent of σ 2 , confirming the result obtained in [3] for the pure noise case.…”
Section: By Identifyingsupporting
confidence: 86%
“…We then havẽ The last part of the thesis follows by the same argument as used in the proof of Theorem 3 in [3].…”
Section: Approximation Of the Condensed Densitymentioning
confidence: 99%
See 1 more Smart Citation
“…In [2] it was proved that, when s = 0, in the limit for n → ∞ the condensed density is a distribution supported on the unit circle and it can be proved [1] that in the limit for σ → ∞ the generalized eigenvalues ξ j tend to concentrate on the unit circle and, in the limit for σ → 0, they concentrate around the true ξ j , j = 1, . .…”
Section: The New Transformmentioning
confidence: 99%
“…We notice first that in order to cope with the Dirac distribution appearing in the definition of S n (z, σ ), it is convenient to use an alternative expression given by (see [2])…”
Section: Theorem 1 If S(z) Is Identifiable From a Thenmentioning
confidence: 99%