The variance of the power density spectrum of periodic signals

Abstract The measurement of the spectrum of periodic signals is generally done by assuming zero variance. However, since the phase is often random, this is not exactly true, though generally the variance is small indeed. In the paper, expressions of the variance of the periodogram-based spectral estimator are derived, in the case of different windows, for periodic and for mixed periodic-Gaussian signals. Some examples are given for the cases when the variance is significant.