  This paper deals with the parametric inference for integrated signals
embedded in an additive Gaussian noise and observed at deterministic discrete
instants which are not necessarily equidistant. The unknown parameter is
multidimensional and compounded of a signal-of-interest parameter and a
variance parameter of the noise. We state the consistency and the minimax
efficiency of the maximum likelihood estimator and of the Bayesian estimator
when the time of observation tends to $\infty$ and the delays between two
consecutive observations tend to 0 or are only bounded. The class of signals in
consideration contains among others, almost periodic signals and also
non-continuous periodic signals. However the problem of frequency estimation is
not considered here.
