Subspectral analysis

Thus, from the expansion coefficients // of a Legendre subspectral analysis according to (3.2.8) the moments Pt(cos9)) of the orientational distribution function can be determined. 

The validity of (3.2.9) is restricted to the symmetries mentioned above, that is to cylindrical molecules, macroscopically uniaxial samples, and r] = 0. For many samples, these conditions are fulfilled when using NMR, because the quadrupole coupling tensor of aliphatic deuterons is often found to be axially symmetric. In wideline NMR, the anisotropy of the magnetic shielding is used. Here the angular resolution is lower, and the calculation has to be extended to include p > 0 [Henl]. In combination with MAS (cf. Section 3.3), the Legendre subspectral analysis has been used successfully for the determination of molecular order in partially ordered polymers [Harl]. 

A useful procedure for analyzing ABX spectra and other more complex systems is that of subspectral analysis. This is based on the fact that many complex spectra can be seen to contain one or more simpler subspectra which readily lend themselves to separate analysis. Thus the AB part of the ABX spectrum can be divided into two AB-type subspectra. 

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