In this paper, we discuss the behavior of a linear classical parametric
amplifier (PA) in the presence of white noise and give theoretical estimates of
the noise spectral density based on approximate Green's functions obtained by
using averaging techniques. Furthermore, we give analytical estimates for
parametric amplification bandwidth of the amplifier and for the noisy
precursors to instability. To validate our theory we compare the analytical
results with experimental data obtained in an analog circuit. We describe the
implementation details and the setup used in the experimental study of the
amplifier. Near the threshold to the first parametric instability, and in
degenerate-mode amplification, the PA achieved very high gains in a very narrow
bandwidth centered on its resonance frequency. In quasi-degenerate mode
amplification, we obtained lower values of gain, but with a wider bandwidth
that is tunable. The experimental data were accurately described by the
predictions of the model. Moreover, we noticed spectral components in the
output signal of the amplifier which are due to noise precursors of
instability. The position, width, and magnitude of these components are in
agreement with the noise spectral density obtained by the theory proposed here