Fourier self deconvolution

The simplest operation that can be undertaken is to remove the decay in its entirety. This is done by multiplying the Fourier domain signal by an exponential function that cancels the decay [i.e., [exp(+7iy x )], as 

The functions used to change the decay functions in FSD increase the noise level faster than do the polynomial functions used for spectral derivatives because exponential functions tend to increase more rapidly at high spatial frequencies than polynomials. As a consequence, the effect on the data at high spatial frequencies in the Fourier domain signal (the region where the SNR is the lowest) is most severe. The general rule is that as the FWHH is narrowed by a factor of 2, the SNR of the spectmm decreases by an order of magnitude. In practice, the 

A problem that arises with this procedure is that the spectrum may easily be over-deconvolved, but the spectroscopist does not recognize this condition. Overdeconvolution occurs when the line has been narrowed to the point that the lineshape takes on distinct characteristics of a sine lineshape that is, it develops sidelobes. If sidelobes from two adjacent peaks are superimposed, a new peak appears in the spectrum. Thus, a simple doublet can easily be rendered into a multiplet. To prevent this, smoothing should be turned off and a section of the baseline around the band to be deconvolved should be monitored. FSD is an interactive operation on modem computing systems, so the bands can be seen to narrow in real time as y  

Over-deconvolution has another insidious effect when the spectrum is being smoothed simultaneously. When spectra are over-deconvolved, the sidelobes that appear may be smoothed to the point that they are often manifested as apparent shoulders on real bands. The effect of over-deconvolution is that many bands seem to have been resolved. One way of checking for this occurrence is to measure the wavenumber difference between successive shoulders. If this difference is constant, it is more likely than not that the shoulders are due to sidelobes and the deconvolution has been performed incorrectly. 

It is common practice in commercial software to incorporate more than one operation into FSD methods. As the SNR decreases so dramatically with a reduction in the FWHH, it is common to add Fourier smoothing (or what is sometimes cziled filtering) to the method. Here an additional apodization function is applied at 

Specify the file on the first page of the dialog box (Fig. 10.48) and select, on the second page of the dialog, the spectral range that will be processed. 

If a spectrum with a spectral resolution of 8 cm is post zerofilled with an additional zerofilling factor of 2, the digital resolution after the interpolation is 4 cm .  

Note that, in both cases, however, the spectral resolution is still 8 cm . To avoid artifacts allow at least 50 more data points on each side of the desired interval. This region should also contain meaningful spectral information. 

In the example given in Fig. 10.49 a post zerofilling factor of 4 was used. 

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In another study, ATPase reconstituted into liposomes was analyzed by infrared attenuated total reflection spectroscopy and the secondary-structure elements of the molecule were determined from the spectra obtained by Fourier self-deconvolution [42]. Gratifyingly, essentially identical secondary-structure estimates for the ATPase were obtained by this entirely different approach, suggesting quite strongly that these secondary-structure estimates are reasonably accurate. Thus, any future models for the structure of the H -ATPase must take this information into account. 

Figure 11 DRIFT spectra of Cu-ZSM-5 at 450 K in 5 kPa CO in Ar. Dashed line is a Fourier self-deconvolution spectrum.

FSD Fourier self-deconvolution microwave-induced plasma... 

Spectral Manipulation Techniques. Many sophisticated software packages are now available for the manipulation of digitized spectra with both dedicated spectrometer minicomputers, as well as larger main - frame machines. Application of various mathematical techniques to FT-IR spectra is usually driven by the large widths of many bands of interest. Fourier self - deconvolution of bands, sometimes referred to as "resolution enhancement", has been found to be a valuable aid in the determination of peak location, at the expense of exact peak shape, in FT-IR spectra. This technique involves the application of a suitable apodization weighting function to the cosine Fourier transform of an absorption spectrum, and then recomputing the "deconvolved" spectrum, in which the widths of the individual bands are now narrowed to an extent which depends on the nature of the apodization function applied. Such manipulation does not truly change the "resolution" of the spectrum, which is a consequence of instrumental parameters, but can provide improved visual presentations of the spectra for study. 

Figure 3-37 Raman spectra of DPPC in the CH stretching region (a) measured with an AOTF followed by Fourier self-deconvolution (b) measured with a dispersive scanning monochromator at 5 cm-1 resolution. The spectra show the features due to methyl and methylene vibrations arising from both the hydrocarbon chain and headgroup portions of the lipind. (Reproduced with permission from Ref. 101.)...

This procedure is called Fourier self-deconvolution, and is an alternative to the digital filters in Section 3.3. 

This work was supported by a grant from the National Science Foundation, t Abbreviations used are as follows. FTIR Fourier transform infrared spectroscopy, ATR attenuated total reflectance, IRE internal reflection element, SATR solution ATR FTIR, FSD Fourier self-deconvolution, PLS partial least-squares analysis, PRESS prediction residual sum of squares from PLS. SECV standard error of calibration values from PLS, PLSl PLS analysis in which each component is predicted independently, PLS2 PLS analysis in which all components are predicted simultaneously. 

Two types of secondary structure analysis were used on the spectra collected in this study. The classic curve-fitting method (13) for analysis of the amide I band, was performed in two stages. The first step in the analysis is band narrowing, which allows visualization of component bands, using derivatization and Fourier self-deconvolution (FSD) (14). 

FSD spectra are frequently curve-fit to obtain an estimate of the secondary structure content of the protein being examined. This is justifiable because, in theory, Fourier self-deconvolution should not affect the relative areas of component bands. In practice however, it was found that this assumption is not valid. The relative areas of bands at the edges of the amide I region are increased by FSD. Therefore the following procedure was used for structural analysis. 

Kauppinen J. K., Moffatt D. J., Mantsch H. H., and Cameron D. G. (1981) Fourier self-deconvolution A method for resolving intrinsically overlapped bands. Appl. Spectroscopy 35 271-276. 

All of these functional groups have a distinctive absorption band in the region, and a Fourier self-deconvolution routine is often used to attempt to resolve the often broad resulting absorbance band to give the best fit of the various species to the composite spectrum. 

W-J Yang, PR Griffiths, DM Byler, and H Susi. Protein Conformation by Infrared Spectroscopy Resolntion Enhancement by Fourier Self-Deconvolution. Appl. Spectrosc. 39 282-287, 1985. 

Figure 8 A) The amide 1 band profile in the FTIR spectrum of p-lactoglobulin in D2O B) the second derivative of the spectrum in A) C) the spectrum in A) after Fourier self-deconvolution with a bandwidth of 13 and k = 2.

Griffith Peter, R., Pierce John, A., Hongjin, G. Curve fitting and Fourier self-deconvolution for the quantitative representation of complex spectra. In H.L.C. Meuzelaar, TL. Isenhour (eds.) Computer Enhanced Analytical Spectroscopy, vol. 2, pp. 29-33. Plenum Press, New York (1990)... 

Interferogram to Spectrum W Inverse FI Pfist Zerofiing Fourier Self-Deconvolution Syn metric FT 5 Ijicm <-> pm, nm... 

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