Fourier backtransform

X(aj) Fourier backtransform of the frequency function X(co) into the time function x(t) ... 

Fig. 11. Fourier backtransformed copper spectra. Steps of Fig. 9. Note that the splitted peak (c) results in a node of a beat at 220 eV, showing an exact compensation between the oxygen and sulfur contributions to the complex backscattering amplitude...

Our starting point is the Fourier backtransformation F pecid) of the specularly reflected intensity hped z) which has to be multiplied with before performing the transformation... 

Figure 7 Model calculations of reflectivities (left column), the Fourier backtransformation using Eq, 2 (center column) and the density profiles (right column). Top row monolayer system. Bottom row low density contrast (10%) bilayer.

The top row demonstrates, that F (d) of the monolayer reflectivity shows only one characteristic length scale at rf=150A which is the film thickness. In contrast, the Fourier backtransformation of the bilayer looks very different even though both... 

Fig. 1.1 The Faber-Ziman Sap k) a, /3 = M, X) and Bhatia-Thornton Su k) (/, / = N, C) partial structure factors for liquid and glassy ZnCl2. The points with vertical (black) error bars are the measured functions in (a) and (c) for the liquid at 332(5) °C [ 16] and in (b) and (d) for the glass at 25(1) °C [15, 16]. The solid (red) curves are the Fourier backtransforms of the corresponding partial pair-distribution functions after the unphysical oscillations at r-values smaller than the distance of closest approach between the centres of two atoms are set to the calculated Unlit at r = 0. The broken (green) curves in (a) are from the polarisable ion model of Sharma and Wilson [63] for the Uquid at 327 °C...

In situ EXAFS of dissolved Ag ions in front of a dissolving Ag electrode (a) with and without Ag dissolution, inset fc -weighted x(k) and (b) T(x(k)k ) to distance space showing first coordination shell. Inset Fourier backtransform of truncated first coordination shell and comparison with simulation (dashed) with R = 0.23 nm, N = 2.15, a = 0.0103. (From Lutzenkirchen-Hecht, D. et al.. Corn ScL, 40,1037,1998.)... 

Figure 7.19 Ni K-edge X-ray absorption spectra for as-isoiated (solid line) and NADH- and H2-reduced (dashed line) samples of the hydrogenase from R. eutropha HI6. (a) Edge region (b) Fourier-filtered EXAFS (backtransform window = I.I-2.6 A). Reprinted with permission from Gu, eta/. (1996) and the American Chemical Society.

Figure 4. First coordination sphere (backtransform window = 1.1-2.7 A) Fourier-filtered Ni K-edge EXAFS spectra from redox-poised Thiocapsa ro-...

Fast Fourier Transform Compression is a method that uses Fourier transformation to decompose spectra into a series of Fourier coefficients, to reduce them, and to backtransform them to achieve a compressed version of the spectrum. 

Figure 5. Data reduction and analysis in EXAFS spectroscopy (A) EXAFS spectrum x k) vs. k after background removal. (B) The solid curve is the weighted EXAFS spectrum k x k) vs. k (after multiplying x(k) by k ). (C) Fourier transformation (FT) of the weighted EXAFS spectrum in (B). (D) Fourier-filtered EXAFS spectrum of the major peak in (C) after backtransforming into k space. The dashed curve represents an attempted fit to the filtered data. (Adapted from B. K. Teo, Accts. Chem. Res. 13, 412 (198), with permission of the American Chemical Society.)...

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