Estimation of Input Pulse Locations From the Response of an All-Pole Transfer System Using Tapered Rank Reduction

When a multipulse input time series is estimated from the response of a transfer system, it is necessary to remove characteristics of the transfer system from the response signal before applying the previously proposed method for estimating the input pulse locations. When the ordinary rank reduction is used to remove the characteristics of the transfer system and to estimate the multipulse input time series, the nonsignificant singular values are sharply cut off by low-order truncation if the system Q (quality factor) is high, and then a large ripple occurs around each pulse location. In order to avoid these difficulties, we propose a new method where the multipulse time series is estimated by a rank reduction using a tapering window in order to sup-press the ripple due to the low-order sharp truncation, and then by applying the pole-estimation method to the inverse Fourier transform of the resultant time series, the pulse locations are accurately estimated. By using the pulse locations as the initial estimates, the maximum likelihood estimates of the pulse locations are obtained. From simulation experiments, these principles are confirmed.