Effect of Finite Sampling on Atmospheric Spectra

Abstract

The effect of a finite averaging time on variances is well known, but its effect on power spectra is less clearly understood. We present numerical solutions for the spectral distortion arising from sampling over a finite time interval T and show that the commonly used filter function (1-sinc²πfT), valid for variances, is a reasonable approximation for power spectra only when T≥ 10τ_m, where / is the cyclic frequency, and τ_m is the dominant time scale of the process. Our results exhibit an increasingly steeper low-frequency roll-off as T decreases relative to τ_m, indicating that the measured spectrum is subject to a greater suppression of the lower frequencies (f < 1/T) than predicted by (1-sinc²πfT). This suppression is, in a sense, compensated by an overestimation of spectral estimates in the frequency range f ≥ 1/T.