Localised Capon spectral estimator with application to the processing of NMR signal

In this paper, we present a localised Capon spectral estimator that exhibits improved ability of resolving closely spaced peaks in the frequency domain. Starting with a unitary transformation using the discrete Fourier transform results in signals of interest being localised to small regions of the spectrum. Therefore, the algorithm uses this fact to construct a covariance matrix with low dimensionality, which can be easily inverted. This reduces the number of samples required to be averaged to produce the covariance matrix and as a result allows the spectrum resolution to be improved. In the simulation results, by comparing with the original Capon, the effectiveness of the novel estimator in resolving close peaks is demonstrated using both simulated undamped exponentials and simulated NMR spectroscopy signal (that is damped exponentials).