Advanced Processing in the Time Domain

Processing in general transforms an original time domain signal s(t) with the aid of some processing function(s) into a manipulated frequency domain signal S (f). Manipulations can be performed either in the time domain ( s(t) = s (t) ) prior to the Fourier transformation, or in the frequency domain (S (f) S (f)) after the Fourier 

NMR data i,s usually processed using one or more processing functions, some of which are applied in the time domain, others in the frequency domain. Each processing function in the time domain f(t) also has its counterpart F(f) in the frequency domain and forms a Fourier pair. In principle the same effect in the final spectrum S (f) may be obtained with a given processing function, applied either in the time or the frequency domain as long as a few important rules are followed when performing the 

With s(t) and f(t) beeing the FID of an NMR signal and a processing function or a second FID respectively and with S(f) and F(f) beeing the corresponding frequency domain counterparts, the following rules govern the manipulation of these Fourier pairs  

The multiplication of the FID s(t) with a factor a is equivalent to a multiplication of the spectrum S(f) with the same factor. This equivalence may be exploited e.g. in spectral editing to obtain multiplicity selective C subspectra from the DEPT-45, DEPT-90 and the DEPT-135 data. The multiplication with the corresponding factors may be performed with the DEPT FIDs or the DEPT spectra. 

The multiplication of an FID s(t) with a second time domain function f(t) i.s not simply the multiplication, but the convolution of the two corresponding frequency domain counterparts. Since a multiplication is much simpler to perform - even for a computer - correction functions to improve spectral quality are almost exclusively applied in the time domain (see below). 

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Many of the fiindamental physical and chemical processes at surfaces and interfaces occur on extremely fast time scales. For example, atomic and molecular motions take place on time scales as short as 100 fs, while surface electronic states may have lifetimes as short as 10 fs. With the dramatic recent advances in laser tecluiology, however, such time scales have become increasingly accessible. Surface nonlinear optics provides an attractive approach to capture such events directly in the time domain. Some examples of application of the method include probing the dynamics of melting on the time scale of phonon vibrations [82], photoisomerization of molecules [88], molecular dynamics of adsorbates [89, 90], interfacial solvent dynamics [91], transient band-flattening in semiconductors [92] and laser-induced desorption [93]. A review article discussing such time-resolved studies in metals can be found in... 

Other processing techniques for analysis of F.t.-i.r. data have been developed in order to obtain the maximum of information from the spectra. The advances made in time-resolved techniques, which sample only a portion of the interferogram, permit obtaining of spectra in the microsecond domain this will lead to additional applications of F.t.-i.r. spectroscopy such as the study of dynamic and kinetic processes. 

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