Spectral Analysis and Time Series - max planck research school ...

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A. Lagg – Spectral Analysis Illustrations autocorrelation function of a rectangular pulse xt xt− autocorrelation function
A. Lagg – Spectral Analysis Power spectral density functions (also called autospectral density functions) describe the general frequency composition of the data in terms of the spectral density of its mean square value f , f f mean square value in frequency range : x 2 f , f = lim T ∞ T 1 ∫ T 0 definition of power spectral density function: G x f = lim f 0 x 2 f , f f xt , f , f 2 dt portion of x(t) in (f,f+∆f) f) = lim f 0 x 2 f , f ≈ G x f f 1 f [ lim T ∞ T 1 ∫ T 0 important property: spectral density function is related to the autocorrelation function by a Fourier transform: G x f = 2∫ −∞ ∞ R x e −i 2 f d = 4∫ 0 ∞ xt , f , f 2 dt] R x cos 2 f d
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