Deconvolved spectra

Figure 13. 29Si-MAS NMR spectra of analcite (left) and zeolite Na-Y (right). Key top, deconvolved spectra middle, 79.5 MHz spectra (400 MHz 1H) and bottom, 17.9 MHz spectra (90 MHz 1H). (Reproduced with permission from Ref. 14. Copyright 1982, J. Magn. ResonJ...

A Deconvolving Spectra with Broadband White Noise Added 195... 

B. Deconvolving Spectra with Band-Limited White Noise Added 196... 

Fig. 18 Effects of digitization of the convolved spectrum z(jc) on deconvolution. Trace (a) is the original spectrum o(x), trace (b) the convolved spectrum i(x). Traces (c)-(f) are the deconvolved spectra after digitizing the convolved spectrum using 6, 8, 10, and 12 bits, respectively.

Figure 5 Deconvolved spectra in the C-H stretching legion for 70 mM SDS solutions under various conditions. The bandwidth is IS cm 1 with triangular apodization and a K factor of two.

Figure 50 Observed and deconvolved spectra of a Novolak-type phenol resin.

A Lorentzian LBF was used in the deconvolution. A deconvolution factor of 100 was chosen in order to achieve a net amplification of 3.4. This value was chosen after trials with deconvolution factors of 50,100 and 1000 in the manner recommended by Kauppinen et al. (52). With a factor of 50, underdeconvolution is observed, while a factor of 1000 results in over-deconvolution and negative side lobes. The deconvolution function amplifies the noise as well, and in order to reduce the noise, apodisation with a Blackman function is performed in conjunction with the deconvolution over the fraction of the interferogram specified by a noise reduction factor. A noise reduction factor of 0.5 was chosen. While the intensities of the deconvolved peaks are higher than those in the original spectra, the relative peak intensities in the deconvolved spectra remain the same as in the original (57). 

FIGURE 6.10 PSD (a) of the NIR spectra of whole-kernel and ground wheat along with the derivative spectrum of whole kernel wheat (b). Tick marks on the whole-kernel spectrum in (a) correspond to the tick marks on the negative peaks of the derivative spectrum in (b). Note the ease with which the deconvolved spectra in (a) compare with the original spectra. 

How do we know if we have over-deconvolved Well, we don t. Neither do we know if our derivative transform produces spurious bands. Both FSD and the derivatization of recorded data are pretty much an art, not a science. One just has to try it and develop a feel for its effect on the data. But here are some guidelines (a) FSD will produce negative lobes when you over-deconvolve a spectrum. If these lobes go below zero, you have probably over-deconvolved, (b) Look at the narrowest bands. If lobe production around the narrow bands look as if they should not be there, then you probably have over-deconvolved, (c) Finally, you can compare deconvolved spectra with derivative spectra. Until you get a feel for FSD you may want to use this security blanket. 

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