Abstract:

An efficient algorithm is proposed to reduce the noise in NMR FID signals based on the real-value discrete Gabor transformation developed in our previous work. As NMR FID signals in the time domain are short oscillating decay signals, the FID signals in Gabor transformation domain (i.e., a joint time-frequency domain) are concentrated in very few number of Gabor transformation coefficients, while the noise is fairly distributed among all the coefficients. Therefore, performing a threshold-limiting work in the transform domain can significantly enhance the NMR  FID signals. The theoretical and experimental analyses presented in this paper show that oversampling Gabor transformation is more suitable for NMR FID signal enhancement than critically-sampling transformation, because the synthesis window and its corresponding analysis window in the oversampling case can have better localization in both time domain and frequency domain than that in the critically-sampling case. Furthermore, the oversampling Gabor transform can lead to higher time and frequency resolution than the critically-sampling one.

Key words: NMR FID signals, oversampling Gabor transformation, signal enhancement algorithms