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picture1_Psdtheory


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File: Psdtheory
Experimental Nonlinear Dynamics Supplemental Handout The Power Spectral Density and the Autocorrelation The autocorrelation of a real, stationary signal x(t) is dened to by Rx(τ) = E[x(t)x(t+τ)]. The ...

icon picture PDF Filetype PDF | Posted on 02 Mar 2023 | 2 years ago
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...Experimental nonlinear dynamics supplemental handout the power spectral density and autocorrelation of a real stationary signal x t is dened to by rx e fourier transform called psd sx f thus z if d question what does it mean why answer this recall that ift dt avoid convergence problems we consider only version observed over nite time w where for then xt has restriction necessary because not all our signals will be square integrable however they which take advantage here c j p cusumano revision february so ifs s ds dtds star denotes complex conjugation compactness fre quency argument been suppressed taking expectation both sides eq letting one sees toactually evaluate above integral variables integration must changed let as already g transformed except limits integra tion using change formula understand means remember holds any imagine computing dierent obtained from experiments on same system each these sample function possible functions since exponential kernel inside can pulled outsi...
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