Abstract
In various signal processing applications, it is desired to appropriately modify a given data set so that the modified data set possesses prescribed properties. The modification of the given data set serves as a preprocessing step of ‘cleaning up’ the data before estimating the values of the signal parameters. In this paper, evaluation and improvement of a signal enhancement algorithm, originally proposed by Tufts, Kumaresan and Kirsteins and recently generalized by Cadzow, are presented. In essence, the newly proposed algorithm first arranges the data in a very rectangular (instead of a square) Hankel structured matrix in order to make the corresponding signal-only data matrix orthogonal to the noise, then computes a minimum variance (instead of a least squares) estimate of the signal-only data matrix and finally restores the Hankel structure of the computed minimum variance estimate. An extensive set of simulations is given demonstrating a significant improvement in resolution performance over Cadzow's method at a comparable parameter accuracy. Moreover, arranging the data in a very rectangular matrix reduces drastically the required computation time. In particular, the newly proposed signal enhancement algorithm can be successfully applied to the quantitative time-domain analysis of Nuclear Magnetic Resonance (NMR) data.
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