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| In [[mathematics]], in the area of [[statistical analysis]], the '''bispectrum''' is a statistic used to search for nonlinear interactions. The [[Fourier transform]] of the second-order [[cumulant]], i.e., the [[autocorrelation]] function, is the traditional [[power spectrum]]. The Fourier transform of ''C''<sub>3</sub>(''t''<sub>1</sub>, ''t''<sub>2</sub>) (third-order [[cumulant]]-generating function) is called the bispectrum or '''bispectral density'''. Applying the [[convolution theorem]] allows fast calculation of the bispectrum <math> B(f_1,f_2)=F^*(f_1+f_2).F(f_1).F(f_2)</math>, where <math>F</math> denotes the Fourier transform of the signal, and <math>F^*</math> its conjugate. | | Hello and welcome. My name is Figures Wunder. In her expert lifestyle she is a payroll clerk but she's always wanted her own company. North Dakota is her birth location but she will have to move one day or another. One of the extremely best things in the globe for me is to do aerobics and now I'm attempting to earn cash with it.<br><br>Here is my page :: [http://xn--299ay03byycca57h.kr/zbxe/?document_srl=319947 장원고시원.kr] |
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| Bispectra fall in the category of ''higher-order spectra'', or ''polyspectra'' and provide supplementary information to the power spectrum. The third order polyspectrum (bispectrum) is the easiest to compute, and hence the most popular.
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| A statistic defined analogously is the ''bispectral coherency'' or ''bicoherence''.
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| Bispectrum and [[bicoherence]] may be applied to the case of non-linear interactions of a continuous spectrum of propagating waves in one dimension.<ref>{{cite journal |author=Greb U, Rusbridge MG
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| |title=The interpretation of the bispectrum and bicoherence for non-linear interactions of continuous spectra |journal=Plasma Phys. Control. Fusion |volume=30 |issue=5 |pages=537–49 |year=1988 |doi=10.1088/0741-3335/30/5/005 |url=http://www.iop.org/EJ/abstract/0741-3335/30/5/005}}</ref>
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| Bispectral measurements have been carried out for [[electroencephalography|EEG]] [[signals (biology)|signals]] monitoring.<ref>{{cite journal |author=Johansen JW, Sebel PS |title=Development and clinical application of electroencephalographic bispectrum monitoring |journal=Anesthesiology |volume=93 |issue=5 |pages=1336–44 |date=November 2000 |pmid=11046224 |doi= |url=http://meta.wkhealth.com/pt/pt-core/template-journal/lwwgateway/media/landingpage.htm?issn=0003-3022&volume=93&issue=5&spage=1336}}</ref>
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| In [[seismology]], signals rarely have adequate duration for making sensible bispectral estimates from time averages.
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| ==See also==
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| [[Trispectrum]]
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| ==References==
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| {{reflist}}
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| *{{cite journal |author=Mendel JM |title=Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications |journal=Proc. IEEE |volume=79 |issue=3 |pages=278–305 }}
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| *[http://www.mathworks.com/matlabcentral/fileexchange/3013 HOSA - Higher Order Spectral Analysis Toolbox]: A [[MATLAB]] toolbox for spectral and polyspectral analysis, and time-frequency distributions. The documentation explains polyspectra in great detail.
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| [[Category:Complex analysis]]
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| [[Category:Integral transforms]]
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| [[Category:Fourier analysis]]
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| [[Category:Time series analysis]]
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| [[Category:Nonlinear time series analysis]]
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