Statistical error due to finite-time averaging
B. Picinbono · Physical Review A · 1977
Previous results concerning statistical errors due to finite-time $T$ averaging in many experiments are made more precise. In particular, we show that the error does not always decrease according to a ${T}^{\ensuremath{-}\frac{1}{2}}$ law as $T\ensuremath{\rightarrow}\ensuremath{\infty}$. In the case of power or correlation function measurements, the departure from a ${T}^{\ensuremath{-}\frac{1}{2}}$ law may be due to an unbounded spectral density for some frequencies, which appears for some physical noises.