Instantaneous frequency based spectral analysis of nuclear magnetic resonance spectroscopy data

Nuclear magnetic resonance spectroscopy signals are modelled as a sum of decaying complex exponentials in noise. The spectral analysis of these signals allowing for their decomposition and the estimation of the parameters of the components is crucial to the study of biochemical samples. This paper presents a novel Gabor filterbank/notch filtering instantaneous frequency (IF) estimator, that enables the extraction of weaker and shorter lived exponentials. This new approach is an iterative procedure where a Gabor filterbank is first employed to obtain a reliable estimate of the IF of the strongest component present. The estimated strongest component is then notch filtered, which un-masks weaker components, and the procedure repeated. The performance of this method was evaluated using an artificial signal and compared to the short time Fourier transform, reassigned STFT, and the original Gabor filterbank approach. The results clearly demonstrate its superiority in uncovering weaker signals and resolving components that are very close to one another in frequency. Furthermore, the new method is shown to be more robust than the ITCMP technique at low signal to noise ratios.