Three parametric representations are developed for approximating a gen
eral nonstationary Gaussian process X(t). The representations: (1) are
based on the Bernstein and other interpolation polynomials, spline fu
nctions, and an extension of a sampling theorem for stationary process
es; (2) consist of finite sums of specified deterministic functions wi
th random amplitudes depending on X(t); and (3) converge to X(t) as th
e number of these functions increases However, their convergence rates
differ. Numerical results for a nonstationary Ornstein-Uhlenbeck proc
ess show that the interpolation polynomials have the slowest rate of c
onvergence. The parametric representations based on spline functions a
nd the extended sampling theorem have similar convergence rates The pa
per also presents methods for generating realizations of X(t) based on
the three parametric models of this process.