An exact finite sample variance expression for a class of frequency function estimates

An explicit expression for the variance of finite sample frequency function estimates is presented. The expression is applicable to models estimated using the least-squares method under the following conditions: 1) the system is in the model set; 2) the model structure is linear in the parameters (c.f. FIR, Laguerre and Kautz models); 3) the measurement noise is white; 4) the number of estimated parameters coincides with the number of non-zero spectral lines of the input. The new variance expression gives insight into how to choose the input spectrum in order to obtain reliable frequency function estimates. In the paper this variance expression is also used to compare FIR modeling with empirical transfer function estimation.