Optimum linear finite-dimensional estimator of signal waveforms

This paper deals with the linear estimation of noise corrupted signal waveforms, from observation over a specified finite time-interval. Two new features are delineated in this paper: 1) the estimating operator is assumed to be finite-dimensional, because economically realizable operators are finite-dimensional in general, and 2) the cost of observation and estimation is taken into account, and assumed to be dependent upon the dimension of the operator only. As a result, the optimum linear finite-dimensional operator that minimizes the risk (the sum of cost and average loss) is obtained for the case in which a quadratic loss function due to error is adopted.