System Laplace-transform estimation from sampled data

This paper presents a method for estimating the Laplace transform of a dynamic system, given its input and output in sampled-data form and corrupted by noise. The estimate is made by first estimating the coefficients of the pulse transfer function relating the input and output and then by converting these estimates to estimates of the Laplace-transform coefficients. Whenever Laplace-transform coefficients are estimated from sampled data, certain knowledge about the signals between the sampling instants must be known a priori or be assumed. In the proposed method this knowledge is used explicitly to relate the coefficients of the Laplace transform to those of the transform. When this knowledge is correct the estimate Laplace-transform coefficients are asymptotically unbiased. As an illustration, the proposed method has been used to estimate the transfer function of a second-order dynamic system. In this example the variances of the estimates have been compared with the Cramer-Rao bound for unbiased estimates.