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Fourier analysis

Authors: Lawson, J.;

Fourier analysis

Abstract

What follows is a description of my analysis. First, the FFT that I use is described on the attached pages. Note that the scaling factor for the forward transform is 1/N. I compute the following rms values: rms(original data) = 64.9463 nm; rms(data*hanning) = 55.7723 nm (before renormalization). The use of the hanning filter is accompanied by a renormalization to insure that the rms value is maintained. I also fit to the curvature of the scan. The data corrected for focus gives the following rms values: rms(corrected data) = 56.8835 nm; rms(corrected data*hanning) = 53.2179 nm (before renormalization). The PSD is shown for various data. The PSD is calculated as: PSD = | FFT(y) | {sup 2} * xl where xl is the length of the x axis, 45.9952. I did find an error in the plot that you were sent. If kx is the frequency axis, i.e., values from (0,Nyquist), then kx(l,Nyquist) is plotted versus PSD(0,Nyquist). This error is corrected in the attached plots. The plot you have appears to be the PSD of the original data with no hanning applied. The removal of the quadratic term appear to have a negligible effect on the PSD. It changes only the first couple of terms (which lie outside of the data valid range). The removal of the center feature has a much stronger effect.

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Keywords

Fourier Analysis, Computers, 99 Mathematics, Law, Information Science, Management, Miscellaneous

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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