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Correlation function Wiener-Khintchine theorem

It is a well known fact, called the Wiener-Khintchine Theorem [gardi85], that the correlation function and power spectrum are Fourier Transforms of one another ... [Pg.305]

The velocity, which equilibrates at large times, is not an aging variable. Thus, Fourier analysis and the Wiener-Khintchine theorem can be used equivalently to obtain the equilibrium correlation function Cvv(t — t2). [Pg.280]

As stated above, the Langevin force F(t) can be viewed as corresponding to a stationary random process. Clearly, the same is true of the solution v(f) of the generalized Langevin equation (22), an equation which is valid once the limit ti —> —oo has been taken. Thus, Fourier analysis and the Wiener-Khintchine theorem can be used to obtain the velocity correlation function, which only depends on the observation time Cvv(t, t2) = Cvv(t —12). As in the classical case, the velocity does not age. [Pg.285]

Applying the Wiener-Khintchine theorem, one obtains the velocity correlation function as the inverse Fourier transform of Cvv ( ), that is, in terms of the noise spectral density CFF([Pg.299]

Now, we consider the important limit of weak laser intensity. In this limit, the Wiener-Khintchine theorem relating the line shape to the one-time correlation function holds. As we shall show now, a three-time correlation function is the central ingredient of the theory of fluctuations of SMS in this limit. In Appendix B, we perform a straightforward perturbation expansion with respect to the Rabi frequency Q in the Bloch equation, Eq. (4.6), to find... [Pg.216]

In this chapter, we developed a stochastic theory of single molecule fluorescence spectroscopy. Fluctuations described by Q are evaluated in terms of a three-time correlation function C iXi, X2, T3) related to the response function in nonlinear spectroscopy. This function depends on the characteristics of the spectral diffusion process. Important time-ordering properties of the three-time correlation function were investigated here in detail. Since the fluctuations (i.e., Q) depend on the three-time correlation function, necessarily they contain more information than the line shape that depends on the one-time correlation function Ci(ti) via the Wiener-Khintchine theorem. [Pg.246]

TJie Fourier transform of the first-order correlation function G r) represents the normalized frequency spectrum of the incident light-wave intensity I (o>) (Wiener-Khintchine theorem) [930, 935]. [Pg.414]

These records have been transformed into the frequency domain by a "Fast-Fourier Transformation" (FFT) and ensemble averaged there. The Fourier Transformation of the resulting array back into the time domain gives the correlation function (4) by the Wiener Khintchine theorem. [Pg.554]

The cross correlation function given in Equation (F6) may be further modified to a form better suited for the two-dimensional correlation analysis with the help of the Wiener-Khintchine theorem [5]. This theorem conveniently relates the cross correlation function with the corresponding Fourier transforms. In the first step, the expression for the dynamic spectrum y(v2, t -I- t) in Equation (F6) is rewritten in terms of the inverse of Fourier transform of y(v2, s )-... [Pg.365]

In general, the energy spectrum is calculated by using the auto-correlation function Rt, (r) based on Wiener-Khintchine s theorem as follows ... [Pg.101]


See other pages where Correlation function Wiener-Khintchine theorem is mentioned: [Pg.203]    [Pg.54]    [Pg.78]    [Pg.367]    [Pg.244]   
See also in sourсe #XX -- [ Pg.299 ]

See also in sourсe #XX -- [ Pg.299 ]




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