  We construct a signal from "almost" pure oscillations within some low
frequency band. We construct it to produce a superoscillation with frequency
above the nominal band limit. We find that indeed the required high frequency
is produced but the signal is not a superoscillation as the high frequency
components are real and result from an intriguing interference in the frequency
domain of the tails of Gaussians concentrated around points within the nominal
frequency band.
