Efficient Estimation of Decaying Sinusoids with Application in NMR Spectroscopy

Sammanfattning: In this thesis, the Wideband Sparse Exponential Mode Analysis (WSEMA) estimator is introduced. It combines two recently developed techniques, the wideband dictionary and the Sparse Exponential Mode Analysis (SEMA) to make for an efficient estimator. WSEMA estimates the parameters of decaying sinusoids, without a priori-information about the number of modes present in the signal. WSEMA works with arbitrary sampling schemes and is therefore compatible with sampling scheme optimization ideas presented recently. The suggested estimator is evaluated using both simulated data and real nuclear magnetic resonance (NMR) spectroscopy data. The results in this thesis sug-gests that WSEMA can be used to efficiently estimate the frequencies and dampings of multi-modal signals with minimum variance, although work remains concerning the handling of closely spaced peaks. Parts of the content in this thesis have been published in the article Computationally Efficient Estimation of Multi-dimensional Damped Modes Using Sparse Wideband Dictionaries, accepted to the 26th European Signal Processing Conference (EUSIPCO 2018).