The resolution enhancement conferred by numerical deconvolution of powder pattern spectra to spectra characteristic of a single alignment greatly simplifies solid state NMR spectral analysis. This is especially beneficial when the spectrum is a superposition of signals from multiple environments or sites of labelling. We have developed an innovative method to deconvolute (depake) spectra governed by axially symmetric second rank tensor interactions which possess a P2(cos[theta]) dependence upon orientation, where [theta] is the angle between the symmetry axis and the external magnetic field. Our approach differs substantially from previously published procedures which are iterative or require matrix inversion and, hence, are slow. The new method, instead, utilizes weighting functions in time and frequency domains to facilitate a rapidly executed solution based upon fast Fourier transformation (FFT). Its efficacy is demonstrated with 2H and 31P NMR data for model membranes.
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