We develop the ideas of irregular sampling applied to the problem of estimation of the impulse response function of a time-invariant continuous linear system using discrete-time input-output cross-correlograms. Even though it may seem that estimation of the impulse response function is similar to that of the correlation function (the response function is recovered through the input-output cross-correlation when the system is enjoyed by a white noise), there is a generic difference between these two functions: the correlation function is always symmetric whereas the impulse response function need not have this property. Moreover, in causal systems the impulse response function equals zero on the negative half-line. Therefore new features in estimation of this function arise. For earlier results on the problem.