A tapered SVD without rank determination for estimation of multipulse input time series from noisy output

One of the key questions to be addressed in this paper is how to estimate the deterministic input multipulse time series from a noisy response of the resonant transfer system in the case where the SNR is low and the system Q (quality factor) of the transfer system is high. By generalizing the sharp truncation employed in the standard singular-value-decomposition (SVD), a tapering window is introduced to truncate high order non-significant singular values obtained by the SVD, the mean squared error of the estimates due to the standard SVD-based estimator is reduced to a minimum. This paper also presents a new method to design an optimum tapering window for estimating multipulse time series