A linear prediction method for accurately estimating the parameters of a rational model of transient-type data is presented. This method makes use of the singular value decomposition of an extended-order autocorrelation-like matrix estimate associated with the time series being analysed. The method is first tested on simulated data consisting of three exponentially damped sinusoids of closely spaced frequencies in additive white Gaussian noise. Next, the method is used to analyse nuclear magnetic resonance (NMR) data.