  The pure time delay operator is considered in continuous and discrete time
under the assumption of the input signal being integrable (summable) with
square. By making use of a discrete convolution operator with polynomial Markov
parameters, a common framework for handling the continuous and discrete case is
set. Closed-form expressions for the delay value are derived in terms of the
Laguerre spectra of the output and input signals. The expressions hold for any
feasible value of the Laguerre parameter and can be utilized for e.g. building
time-delay estimators that allow for non-persistent input. A simulation example
is provided to illustrate the principle of Laguerre-domain time delay modeling
and analysis.
