Filters Fourier transform

On the other hand, the monochromator has the great advantage that it automatically eliminates the Ka3i4-satellites. Fig. 6 demonstrates that this can be achieved as well with the help of a Fourier transform filtering program, allowing a satellite free spectrum also for Magnesium irradiation where monochromatization with the help of a spherically bent quartz crystal so far has not been shown. 

Fig. 6. Elimination of Ka3 4-satellites in the C lr-spectrum of paraffin. The raw data in Fig. 6 A are transformed with the help of the Fourier transform filtering procedure into the satellite-free spectrum in Fig. 6 B. For details see example in Fig. 7...

One solution to the problem is to increase the ionization probability. This can be done by choosing primary ions with heavy mass, for example, Bi+ or even Ccarbon atoms. The noise level can also be reduced by techniques of digital image processing. For example, a fast Fourier transform technique has been used to remove noise from the image. This technique transforms an image from a space domain to a reciprocal domain by sine and cosine functions. Noise can be readily filtered out in such domain. After a reverse Fourier transform, filtered data produces an image with much less noise. 

Divinylbenzene-hydrophilic methacrylate copolymer 944 DNOC 1350 Domesticine 1064 DOtz benzannulation 454-459 Double Fourier transform filtering 984, 985 DRD 953 Drinking water,... 

Fourier transform filter 929, 981 Fourier transform IR spectroscopy 547 Fractionation factors 367 Fragmentation, metastable 275 Franck-Condon simulation 107 FRAP (ferric reducing abiUty of plasma) assay 857... 

Figure 28. In situ atomically resolved STM images of n-InP(l 11) obtained in I FSi), solution, (a) Unfiltered top view, (b) Image after application of Fourier transform filtering method. Reproduced with permission from Ref. 258, Copyright (1998) The Electrochemical Society.

There are also other procedures, but these are not as well documented. These procedures are delineated in this chapter. The image analysis is quite varied and covers a wide range of possibilities. Filtering techniques include both high and low frequency as well as two-dimensional Fourier transform filtering. Scrupulous preparation and extreme care yield excellent images. 

In order to remove noise by Fourier-transform filtering we can look at the transform, as in Fig. 7.2-6. However, it is often more convenient to inspect the power spectrum, which is a (usually semi-logarithmic) plot of the magnitude (i.e., of the square root of the sum of squares of the real and imaginary components) of the Fourier transform. Such a power spectrum is shown in Fig. 7.2-9, both for a noise-free signal, and for the same signal with noise. The power spectrum is symmetrical, i.e., the information at negative and... 

In Figure 13, a typical high resolution contact mode SFM scan of uniax-ially oriented POM is shown together with the corresponding 2-D fast Fourier transform filtered image (139). Since the polymer chain direction is in this particular case known a priori, the observed periodicities can be related to the well-established hexagonal crystal structure of POM in a straightforward manner. Uniaxially oriented or epitaxially crystallized specimens thus help in the analysis of the data, as has been discussed in recent review articles (140,141). 

Smoothing by Fourier transform filtering is more arduous with respect to programming computation and time, but this algorithm is now being used time by time. 

Most modern infrared and NMR spectrometers collect data in the time domain with interferometers, and then the data are transformed to the familiar frequency domain by the Fourier transform. Filtering and signal enhancement in the Fourier domain before transformation is often an attractive approach to signal processing. 

Bowen, W. R., and Doneva, T. A. (2000). Artefacts in AFM studies of membranes Correcting pore images using fast fourier transform filtering. J. Membr. Sci. 171, 141. 

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