Spectral variance estimation and the analysis of turbulence data
K. N. Helland, M. Rosenblatt · The Physics of Fluids · 1979
The results of an asymptotic analysis for the variance of power spectra and the real and imaginary parts of complex cross spectra are presented. The formulae for the spectral variances do not require an assumption of jointly Gaussian probability density functions for the time series and, therefore, are of special importance to the analysis of turbulence data. The variances computed from the asymptotic formulae compare favorably with directly estimated variances for power spectra and a third-order cross spectrum which appear in the study of spectral energy transfer in turbulent flows. The asymptotic variance formulae can be useful tools for the design of experiments which require estimation of power and cross spectra.