  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 time
sampled FID signal is well modeled as a finite mixture of exponential sequences
plus noise. We propose to use the Hilbert-Huang Transform (HHT) for noise
reduction and characterization, where the generalized Hilbert-Huang represents
a way to decompose a signal into so-called intrinsic mode function (IMF) along
with a trend, and obtain instantaneous frequency data. Moreover, the HHT for an
FID signal's feature analysis is applied for the first time. First, acquiring
the actual untuned FID signal by a developed prototype of proton magnetometer,
and then the empirical mode decomposition (EMD) is performed to decompose the
noise and original FID. Finally, the HHT is applied to the obtained IMFs to
extract the Hilbert energy spectrum, to indicate the energy distribution of the
signal on the frequency axis. By theory analysis and the testing of an actual
FID signal, the results show that, compared with general noise reduction
methods such as auto correlation and singular value decomposition (SVD),
combined with the proposed method can further suppress the interfered signals
effectively, and can obtain different components of FID signal, which can use
to identify the magnetic anomaly, the existence of groundwater etc. This is a
very important property since it can be exploited to separate the FID signal
from noise and to estimate exponential sequence parameters of FID signal.
