A statistical test to discern random from constant amplitude harmonics

Periodogram is an important tool to reveal hidden periodicities in a given time series but does not tell whether the resulting spectral lines are associated with constant or random amplitude harmonics. Applications dealing with random amplitude models include Doppler spread targets and detection in the presence of fading. We propose to estimate the variance of the harmonic amplitude and then make the decision based on whether the variance can be regarded as zero in a statistical sense. This is a viable approach because any constant has variance zero whereas any real random process has a positive variance. A rigorous statistical test is formulated and illustrated with simulations.