A probability inequality for band-limited pulse trains

Band-limited pulse trains derived from a discrete stochastic process are considered. An upper bound is obtained for the average probability that the magnitude of the departure of the instantaneous signal value from the mean signal value exceeds
\lambda
times the standard deviation, as a function of
\lambda
. This upper bound is useful in the analysis and prediction of intersymbol interference, quantizing errors, and digit errors in digital data communication systems.