Detection of Aliasing in Persistent Signals

We explain why aliasing can be detected in a generic temporally-sampled stationary signal process. We then define a concept of stationarity that makes sense for single waveforms. (This is done without assuming that the waveform is a sample path of some underlying stochastic process.) We show how to use this concept to detect aliasing in sampled waveforms. The constraint that must be satisfied to make detection of aliasing possible is shown to be fairly unrestrictive. We use simple harmonic signals to elucidate the method. We then demonstrate that the method works for continuous-spectrum signals---specifically, for time series from the Lorenz and Rossler systems. Finally we explain how the method might permit the recovery of additional information about Fourier components outside the Nyquist band.