26 May 2000 Ž . Chemical Physics Letters 322 2000 341–350 www.elsevier.nlrlocatercplett High resolution, high sensitivity proton NMR spectra of solids obtained using continuous wavelet transform analysis Shangwu Ding, Charles A. McDowell ) Department of Chemistry, UniÕersity of British Columbia, 2036 Main Mall, VancouÕer, BC V6T 1Z1, Canada Received 22 November 1999; in final form 10 April 2000 Abstract Ž . Ž . The application of continuous wavelet transform CWT analysis to the free-induction decay FID signals of SPEDA Ž . s ingle p ulse e xcitation with delayed acquisition solid state NMR spectroscopy is demonstrated to yield high sensitivity, high resolution, phase corrected and quantitative proton spectra, without using homonuclear decoupling or high speed Ž . sample rotation. Moreover, a better description of the spin dynamics the time evolution of the resonance frequencies can be obtained from the CWT spectrogram. Three typical polycrystalline compounds are used to verify the versatility of this technique which generates spectra with the same, or higher, quality on comparison with those obtained using the CRAMPS Ž . combined r otation and multiple p ulse s pectroscopic technique. q 2000 Elsevier Science B.V. All rights reserved. 1. Introduction Ž . Wavelet transform WT is a method for analyz- ing the time-frequency characteristics of non-sta- tionary signals and has been found to be important in w x many disciplines 1–11 . In particular, it has been shown to be potentially significant in the study of w x solution NMR 12–15 , multiple-quantum filtered 23 w x w x NMR of Na ions in gels 16 , solid state NMR 17 , w x and NMR imaging 18,19 . The most significant feature of a wavelet transform is that it is predicated on the fact that an oscillating signal of a certain frequency often has a finite lifetime rather than an Ž . infinite one, as Fourier transform FT theory implic- itly presumes. Thereby, a WT analysis may yield a more accurate representation than does a FT treat- ) Corresponding author. Fax: q 1-604-8222847; e-mail: mcdowell@chem.ubc.ca ment of the real physical processes of a practical system. This is the case for, e.g., a vibrating acousti- cal fork or a free decaying nuclear magnetization vector, neither of which is maintained for an in- finitely long time. Although NMR studies usually focus on the resonant frequencies and FT seems generally to be a sufficiently powerful and simple protocol, when it is paramount to obtain more infor- mation about spin dynamics, phase distortions and sensitivities, WT analysis may offer a different per- spective and yield more precise information about the details of the various physical processes. The wavelet transform analysis method when ap- plied to a non-stationary signal, e.g., a NMR FID, transforms the input data from a time domain into a time-frequency domain. Thus a WT translates the signal representation into a set of functions, all de- rived from a unique prototype called a wavelet, which is assumed to be well-localized in both the 0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 00 00447-4