Topic
Spectral density estimation
About: Spectral density estimation is a research topic. Over the lifetime, 5391 publications have been published within this topic receiving 123105 citations.
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TL;DR: In this article, a quasi-likelihood or minimum contrast-type method for the parameter estimation of random fields in the frequency domain based on higher-order information is proposed, which uses the spectral density of the general kth order and allows for possible longrange dependence in the random fields.
Abstract: This paper provides a quasi-likelihood or minimum-contrast-type method for the parameter estimation of random fields in the frequency domain based on higher-order information. The estimation technique uses the spectral density of the general kth order and allows for possible long-range dependence in the random fields. To avoid bias due to edge effects, data tapering is incorporated into the method. The suggested minimum contrast functional is linear with respect to the periodogram of kth order, hence kernel estimation for the spectral densities is not needed. Furthermore, discretization is not required in the estimation of continuously observed random fields. The consistency and asymptotic normality of the resulting estimators are established. Illustrative applications of the method to some problems in mathematical finance and signal detection are given.
26 citations
Book•
01 Nov 2002
TL;DR: In this paper, the Toeplitz and Wiener algebras of operator matrices of almost periodic matrix functions are extended with positive extensions in the Wiener classes.
Abstract: Introduction Abstract band method: New variations Toeplitz and Wiener algebras of operator matrices Positive extensions in Wiener classes of almost periodic matrix functions Appendix Bibliography Index.
26 citations
TL;DR: The algorithm uses discrete, parametric signal models in z-space, whose parameters are determined by a two step identification algorithm to develop a method for the supervision and fault diagnosis of dynamic systems.
26 citations
TL;DR: For a trigonometric polynomial of large sparsity, a new sparse fast Fourier transform is presented by shifted sampling and using MUSIC resp.
Abstract: In spectral estimation, one has to determine all parameters of an exponential sum for finitely many (noisy) sampled data of this exponential sum. Frequently used methods for spectral estimation are MUSIC (MUltiple SIgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique). For a trigonometric polynomial of large sparsity, we present a new sparse fast Fourier transform by shifted sampling and using MUSIC resp. ESPRIT, where the ESPRIT based method has lower computational cost. Later this technique is extended to a new reconstruction of a multivariate trigonometric polynomial of large sparsity for given (noisy) values sampled on a reconstructing rank-1 lattice. Numerical experiments illustrate the high performance of these procedures.
26 citations
25 Oct 1994
TL;DR: In this article, the authors present explicit bias and variance expressions for quadratic TF-invariant estimators of an expected real-valued QTFI representation based on a single noisy observation.
Abstract: We study time-varying spectral estimation for nonstationary processes with restricted time-frequency (TF) correlation. We present explicit bias and variance expressions for quadratic TF-invariant (QTFI) estimators of an expected real-valued QTFI representation based on a single noisy observation. Unbiased theoretical estimators with globally minimal variance are derived and approximately realized by a matched multiwindow method. >
26 citations