Use of Autocorrelation-Like Function to Improve the Performance of Linear-Prediction Parameter Estimators

Abstract

In this work, a novel approach to the usage of an autocorrelation function in order to improve signal-to-noise ratio (SNR) is presented. This method avoids the usual problems entailed by standard autocorrelation function-based approaches to nonstationary signals such as NMR signals. The Cadzow autocorrelation matrix approach to transient data is often not suitable for time-domain signal analysis; in fact, it does not maintain the Hankel structure of the prediction matrix, which is mandatory for many linear-prediction (LP) applications. The approach presented here conserves the Hankel structure of the prediction matrix and, moreover, does not change the frequency and linewidth parameters of the signal components. Furthermore, the proposed autocorrelation-like function permits a weighting of the individual components according to theirT₂decay constant. This property opens new possibilities for retrieving signal parameters by LP procedures. These new procedures are applied to simulated 2D signals and 1D NMR measurements of phosphorus metabolites in frog muscle.