We study asymptotic behavior of the averaged integrals of a Lévy-driven
linear process weighted by a complex exponent of polynomials with real coefficients.
Such functionals naturally arise in the problems relating to nonlinear regression
analysis and signal processing, specifically in the estimation of parameters of
frequency-modulated signals.
Under some conditions on the Lévy process and kernel defining the linear process,
we get a uniform strong law of large numbers for this weighted process. More
precisely, it is shown that the considered integrals converge a.s. to zero uniformly
over all the values of the real coefficients of the polynomials of fixed order.
The result obtained is then used to prove strong consistency of LSE for the
parameters of linearly-modulated trigonometric signal (chirp signal) observed against
the background of shot noise described above.