Discusses the appearance of peaks and valleys in Allan deviation plots (also known as sigma-tau, root Avar, or Adev plots). This distinctly oscillatory pattern, especially at long-term /spl tau/-values, usually means the presence of quasi-sinusoidal frequency modulation of an oscillator's signal. However, quasi-sinusoidal oscillatory behavior in sigma-tau plots at long /spl tau/ may be due to statistical sampling and not to actual oscillator or clock data. Periodic variations in sigma-tau plots are often used as an indicator of periodic environmental perturbations such as a diurnal or other external influence, and it is important to know whether these variations are an analytical artifact or not. Removal of drift can make the oscillatory pattern worse. Samples of clock data for a dispersive noise process look like a portion of a sinusoid because the sample duration is less than the inverse of the data's inherent low frequency extent. Drift removal also removes low frequency components of noise, which causes negative bias of root Avar at long tau. The root Avar and drift-removal transfer functions have peaks and nulls that interfere with each other and can cause an oscillatory pattern in the resulting sigma-tau plot.