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The parameters in a nuclear magnetic resonance (NMR) free induction decay(FID) signal contain information that is useful in magnetic field measurement,magnetic resonance sounding (MRS) and other related applications. A real timesampled FID signal is well modeled as a finite mixture of exponential sequencesplus noise. We propose to use the Hilbert-Huang Transform (HHT) for noisereduction and characterization, where the generalized Hilbert-Huang representsa way to decompose a signal into so-called intrinsic mode function (IMF) alongwith a trend, and obtain instantaneous frequency data. Moreover, the HHT for anFID signal's feature analysis is applied for the first time. First, acquiringthe actual untuned FID signal by a developed prototype of proton magnetometer,and then the empirical mode decomposition (EMD) is performed to decompose thenoise and original FID. Finally, the HHT is applied to the obtained IMFs toextract the Hilbert energy spectrum, to indicate the energy distribution of thesignal on the frequency axis. By theory analysis and the testing of an actualFID signal, the results show that, compared with general noise reductionmethods such as auto correlation and singular value decomposition (SVD),combined with the proposed method can further suppress the interfered signalseffectively, and can obtain different components of FID signal, which can useto identify the magnetic anomaly, the existence of groundwater etc. This is avery important property since it can be exploited to separate the FID signalfrom noise and to estimate exponential sequence parameters of FID signal.

Application of Hilbert-Huang decomposition to reduce noise and characterize for NMR FID signal of proton precession magnetometer