ANALYSIS OF THE REDOR SIGNAL AND INVERSION

An inversion of the REDOR signal to recover the dipolar couplings has been recently proposed [K. T. Mueller et al., Chem. Phys. Lett. 242, 5 35 (1995)]: The corresponding integral transform was performed by tabu lation of the kernel followed by numerical integration. After explicit determination of the inverse REDOR kernel by the Mellin transform met hod, we propose an alternative inversion method based on Fourier trans forms, Representation of the inverse REDOR kernel by its asymptotic ex pansion reveals that the inverse REDOR operator is essentially a weigh ted sum of a cosine transform and of its derivative. Consequently, kno wn properties of Fourier transforms can easily be transposed to the RE DOR inversion, allowing for a precise discussion of the value of the m ethod. Moreover, the first term of the asymptotic expansion leading to a derivative of a cosine transform, the REDOR inversion is found to b e extremely sensitive to noise, thus considerably reducing the useful part of the theoretical dipolar window, (C) 1998 Academic Press.