Signal Reconstruction in Unstable Magnetic Field NMR with Wavelet Analysis

Abstract

Recently, wavelet analysis has become a powerful tool and is widely used in nuclear magnetic resonance (NMR) signal processing. Wavelet transform can not only give the wavelet energy spectrum of NMR signals, but also give multiple characteristics of the signals, such as center frequency, maximum energy, and energy duration. Usually, wavelet transform is used in stable magnetic field NMR. In this paper, we survey its application in processing NMR signal from unstable magnetic field. The results show that in unstable magnetic field, the signal's crucial information can be obtained through the wavelet energy spectrum, such as the intensity, the chemical shift, the frequency fluctuation range, the energy, and the scale of the maximal energy, and so on. Based on these knowledge, the signal can be reconstructed using the reference deconvolution, with unstable field effect greatly suppressed.

Mathematical and Statistical Review of NMR Time Domain Data Pre-Processing

“…The fourth method is the wavelet transform 45 , which is less commonly used but advantageous for handling uneven frequencies. Unlike the Fourier transform, which assumes constant frequencies, the wavelet transform can handle uneven frequency data, making it useful for FIDs affected by eddy currents (as discussed in section " Eddy Current (EC) Correction").…”

Mathematical and Statistical Review of NMR Time Domain Data Pre-Processing

“…The fourth method is the wavelet transform 45 , which is less commonly used but advantageous for handling uneven frequencies. Unlike the Fourier transform, which assumes constant frequencies, the wavelet transform can handle uneven frequency data, making it useful for FIDs affected by eddy currents (as discussed in section " Eddy Current (EC) Correction").…”