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Modern Spectral Estimation: Theory and Application

01 Jan 1988-
About: The article was published on 1988-01-01 and is currently open access. It has received 2657 citations till now. The article focuses on the topics: Spectral density estimation.
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Book
16 Mar 2001

7,058 citations

Book
01 Feb 2006
TL;DR: Wavelet analysis of finite energy signals and random variables and stochastic processes, analysis and synthesis of long memory processes, and the wavelet variance.
Abstract: 1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.

2,734 citations

Book
01 Jan 2005
TL;DR: 1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra.
Abstract: 1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra. 4. Parametric Methods for Line Spectra. 5. Filter Bank Methods. 6. Spatial Methods. Appendix A: Linear Algebra and Matrix Analysis Tools. Appendix B: Cramer-Rao Bound Tools. Appendix C: Model Order Selection Tools. Appendix D: Answers to Selected Exercises. Bibliography. References Grouped by Subject. Subject Index.

2,620 citations


Cites background or methods from "Modern Spectral Estimation: Theory ..."

  • ...More detailed information on these and other windows can be found in [Harris 1978; Kay 1988; Marple 1987; Oppenheim and Schafer 1989; Priestley 1981; Porat 1997], where many of the closed–form windows have been compiled....

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  • ...It should be noted, however, that the case of ARMA signals with zeroes near the unit circle is a difficult one for all known ARMA estimation methods [Kay 1988; Marple 1987; Söderström and Stoica 1989]....

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  • ...Second, the LS method has been found to be more accurate than the Yule– Walker method in the sense that the estimated parameters of the former are on the average closer to the true values than those of the latter [Marple 1987; Kay 1988]....

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  • ...The previous and other applications of spectral analysis are reviewed in [Kay 1988; Marple 1987; Bloomfield 1976; Bracewell 1986; Haykin 1991; Haykin 1995; Hayes III 1996; Koopmans 1974; Priestley 1981; Percival and Walden 1993; Porat 1994; Scharf 1991; Therrien 1992; Proakis, Rader, Ling, and Nikias 1992]....

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  • ...2); they require about twice the computational burden of the LDA algorithm (see [Marple 1987; Kay 1988; Söderström and Stoica 1989])....

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Journal ArticleDOI
TL;DR: The presented exploratory approach of mapping influences between a region of interest and the rest of the brain can form a useful complement to existing models of effective connectivity.

1,026 citations


Cites background from "Modern Spectral Estimation: Theory ..."

  • ...The discrete zero-mean vector time-series x[n] = (x1[n], . . ., xM[n]) T can be modeled as a vector autoregressive (VAR) process of order p (e.g., Kay, 1988): x n½ ¼ Xp i¼1 A i½ x n i½ þ u n½ where u[n] is (multivariate) white noise....

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Journal ArticleDOI
TL;DR: The strengths and limitations of correlation-based signal processing methods, with emphasis on the bispectrum and trispectrum, and the applications of higher-order spectra in signal processing are discussed.
Abstract: The strengths and limitations of correlation-based signal processing methods are discussed. The definitions, properties, and computation of higher-order statistics and spectra, with emphasis on the bispectrum and trispectrum are presented. Parametric and nonparametric expressions for polyspectra of linear and nonlinear processes are described. The applications of higher-order spectra in signal processing are discussed. >

931 citations


Cites background from "Modern Spectral Estimation: Theory ..."

  • ...…one of the aforementioned techniques has certain advantages and limitations not only in terms of estimation performance but also in terms of computational complexity and, therefore, depending on the signal environment, one has to choose the most appropriate [Marple, 1987; Kay, 1988; Haykin, 19831....

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