  Spectra derived from fast Fourier transform (FFT) analysis of time-domain
data intrinsically contain statistical fluctuations whose distribution depends
on the number of accumulated spectra contributing to a measurement. The tail of
this distribution, which is essential for separation of the true signal from
the statistical fluctuations, deviates noticeably from the normal distribution
for a finite number of the accumulations. In this paper we develop a theory to
properly account for the statistical fluctuations when fitting a model to a
given accumulated spectrum. The method is implemented in software for the
purpose of automatically fitting a large body of such FFT-derived spectra. We
apply this tool to analyze a portion of a dense cluster of spikes recorded by
our FST instrument during a record-breaking event that occurred on 06 Dec 2006.
The outcome of this analysis is briefly discussed.
