Modern Spectrum Analysis in Multidimensional NMR Spectroscopy:  Comparison of Linear-Prediction Extrapolation and Maximum-Entropy Reconstruction

Abstract

NMR spectroscopy is an inherently insensitive technique, and many challenging applications such as biomolecular studies operate at the very limits of sensitivity and resolution. Advances in superconducting magnet, cryogenic probe, and pulse sequence technologies have resulted in dramatic improvements in both sensitivity and resolution in the past decade. Conversely, the signal-processing method used most widely in NMR spectroscopy, extrapolation of the time domain signal by linear prediction (LP) followed by discrete Fourier transformation (DFT), was developed in the early 1980s and has not been subjected to detailed scrutiny for its impact on sensitivity and resolution. Here we report the first systematic investigation of the accuracy and precision of spectra obtained by LP extrapolation followed by DFT. We compare the results to spectra obtained by maximum-entropy (MaxEnt) reconstruction, which was developed contemporaneously to LP extrapolation but is not widely employed in NMR spectroscopy. Although it reduces truncation artifacts and increases the amplitudes of strong peaks, we find that LP extrapolation generates false-positive peaks and introduces frequency errors. These defects of LP extrapolation become less pronounced for longer data records and higher signal-to-noise ratio. MaxEnt generally yields more detectable peaks for a given number of data samples, more accurate peak frequencies, and fewer false-positive peaks than LP extrapolation. MaxEnt also permits the use of nonlinear sampling, which can give dramatic improvements in resolution. These results show that the use of MaxEnt together with nonlinear sampling, rather than LP extrapolation, could reduce the amount of instrument time required for adequate sensitivity and resolution by a factor of 2 or more.

The advantages of forward linear prediction over multiple aliasing for obtaining high‐resolution HSQC spectra in systems with extreme spectral crowding

“…This appears to contradict the recent conclusions of Stern et al 7 that linear prediction gives unreliable frequency prediction and missed real peaks while also predicting false peaks in crowded spectra. However, different conditions were used in the previous work, including significantly fewer time increment spectra, and a much larger number of frequency coefficients were used in the linear prediction.…”

“…However, different conditions were used in the previous work, including significantly fewer time increment spectra, and a much larger number of frequency coefficients were used in the linear prediction. 7 In addition, the signal-to-noise ratio appeared to be poorer. Furthermore, they mentioned that linear prediction gives better results with better signal-to-noise ratio and more time increment spectra and that using fewer coefficients would give more accurate frequencies and fewer false peaks, at the expense of missing more real peaks.…”

The Elicitation of Plant Innate Immunity by Lipooligosaccharide of Xanthomonas campestris

“…In all heteronuclear experiments, the data matrix was extended to 2048 ϫ 1024 points using forward linear prediction extrapolation (22).…”

Application of Non-uniform Sampling to Three Dimensional Carbon Direct-detection NMR Experiment

“…To process the NUS data, multidimensional Fourier transformation (MFT) 5 and the maximum entropy (MaxEnt) 6 algorithms by using in-house written MFT processing program (J-G. Jee, unpublished data) and the Rowland NMR Toolkit (version 3.0), respectively, were employed. For conventional fast discrete Fourier transformation (FFT) processing and analyses of spectra, NMRPipe software 7 was used.…”