title: "Ersatz" and "hybrid" NMR spectral estimates using the filter diagonalization method.
abstract: The filter diagonalization method (FDM) is an efficient and elegant way to make a spectral estimate purely in terms of Lorentzian peaks. As NMR spectral peaks of liquids conform quite well to this model, the FDM spectral estimate can be accurate with far fewer time domain points than conventional discrete Fourier transform (DFT) processing. However, noise is not efficiently characterized by a finite number of Lorentzian peaks, or by any other analytical form, for that matter. As a result, noise can affect the FDM spectrum in different ways than it does the DFT spectrum, and the effect depends on the dimensionality of the spectrum. Regularization to suppress (or control) the influence of noise to give an "ersatz", or EFDM, spectrum is shown to sometimes miss weak features, prompting a more conservative implementation of filter diagonalization. The spectra obtained, called "hybrid" or HFDM spectra, are acquired by using regularized FDM to obtain an "infinite time" spectral estimate and then adding to it the difference between the DFT of the data and the finite time FDM estimate, over the same time interval. HFDM has a number of advantages compared to the EFDM spectra, where all features must be Lorentzian. They also show better resolution than DFT spectra. The HFDM spectrum is a reliable and robust way to try to extract more information from noisy, truncated data records and is less sensitive to the choice of regularization parameter. In multidimensional NMR of liquids, HFDM is a conservative way to handle the problems of noise, truncation, and spectral peaks that depart significantly from the model of a multidimensional Lorentzian peak.
authors.affiliation: Chemistry Department, University of California, Irvine, California 92617-2025, USA.
authors.forename: Clark D
authors.initials: CD
authors.lastname: Ridge
authors.forename: A J
authors.initials: AJ
authors.lastname: Shaka