Get started
Work

Equivalence of the time‐domain matched filter and the spectral‐domain matched filter in one‐dimensional NMR spectroscopy

Year: 2010
Type: article
Abstract: A type of "matched filter" (MF), used extensively in the processing of one-dimensional spectra, is defined by multiplication of a free-induction decay (FID) by a decaying exponential with the same time constant as that of the FID. This maximizes, in a sense to be defined, the signal-to-noise ratio (SNR) in the spectrum obtained after Fourier transformation. However, a different entity known also as the matched filter was introduced by van Vleck in the context of pulse detection in the 1940's and has become widely integrated into signal processing practice. These two types of matched filters appear to be quite distinct. In the NMR case, the "filter", that is, the exponential multiplication, is defined by the characteristics of, and applied to, a time domain signal in order to achieve improved SNR in the spectral domain. In signal processing, the filter is defined by the characteristics of a signal in the spectral domain, and applied in order to improve the SNR in the temporal (pulse) domain. We reconcile these two distinct implementations of the matched filter, demonstrating that the NMR "matched filter" is a special case of the matched filter more rigorously defined in the signal processing literature. In addition, two limitations in the use of the MF are highlighted. First, application of the MF distorts resonance ratios as defined by amplitudes, although not as defined by areas. Second, the MF maximizes SNR with respect to resonance amplitude, while intensities are often more appropriately defined by areas. Maximizing the SNR with respect to area requires a somewhat different approach to matched filtering.
DOI: 10.1002/cmr.a.20162
Language: English
Subfield: Spectroscopy
Field: Chemistry
Open Access status: green
OpenAlex ID: W1999225913
FWCI: 0.276
Cites: 13
Cited by: 25
Related to: 10