Unique estimates of the parameters of a continuous stationary stochastic process

Explicit parametric relations are derived between the parameters of a continuos time stationary stochastic process governed by a second-order linear differential equation and its uniformly sampled discrete representation. These relations are used to analyze and resolve the multiplicity of the parameters of the continuous process estimated from sampled data, leading to alias-free estimates of spectra. A limiting case of the sampled process, including integrated random walk, is pointed out. The estimation procedure is illustrated by data obtained from a mechanical system.