Statistical Stability in spectrum analysis

Some very simple results which are of use in designing the smoothing system for a digital spectrum analyser, to reduce fluctuations due to the random nature of the envelope of the output of a narrow-band filter are deduced. The `signal/noise ratio¿, defined on a mean square basis, of each observation of envelope-squared is unity. The smoothing schemes operate by averaging several observations of envelope-squared, taken at different times or at different frequencies. The discussion shows the relative insensitivity of the result to fine details of the averaging system.