  We present an integral transformation capable of extracting moments of
arbitrary Paley-Wiener entire functions against a given spectral distribution
based solely on short-time values of the correlation function in a small open
disk about the origin. The integral is proven to converge absolutely to the
expected result for those correlation functions that can be extended
analytically to the entire complex plane, with the possible exception of two
branch cuts on the imaginary axis. It is only the existence of an analytic
continuation that is required and not the actual values away from the small
disk about the origin. If the analytic continuation exists only for a strip
|Im(z)| < \tau_0, then the integral transformation remains valid for all
Paley-Wiener functions obtained by Fourier-Laplace transforming a compactly
supported distribution, with the support included in the interval (-2\tau_0,
2\tau_0). Finally, if the support of the distribution is contained in the
interval $(-\tau_0, \tau_0)$, then the generalized moment can be evaluated from
the short-time values of the correlation function exponentially fast
