An estimate of the variation of a band-limited process

Upper and lower bounds are established for the mean-square variation of a stationary processX(t)whose power spectrum is bounded byomega_{c}, in terms of its average powerP_{0}and the average powerP_{1}of its derivative. It is shown thatleft( frac{2}{pi} right)^{2} P_{1} tau^{2} leq E {|X(t+tau )-X(t)|^{2}} leq P_{1} tau^{2} leq omega_{c}^{2}P_{0}tau^{2}where the upper bounds are valid for anytauand the lower bound fortau < pi / omega_{c}. These estimates are applied to the mean-square variation of the envelope of a quasi-monochromatic process.