A new expression for the variance of scalar frequency
functions estimated using the least-squares method
is presented. The expression is valid for finite sample size and for
a class of model structures, which includes finite impulse response,
Laguerre and Kautz models,
when the number of estimated parameters coincides with the number of
excitation frequencies of the input. The expression
gives direct insight into how excitation frequencies and amplitudes
affect the accuracy of frequency function estimates. The relevance of
the expression when more excitation frequencies are used is also
discussed.