But surely, when narrowband filtering is in place - as any narrow 
  band mode will of necessity be doing internally - any wideband non Gaussian or 
  bursty noise when applied to this narrow filter will eventually become 
  Gaussian IN THAT BANDWIDTH
  
  We first ealised this in teh original QRSS tests with G3PLX back in the 
  1990's.   73kHz was full of spikes and 'crud' from teh then existing 
  Decca signals and other stuff.   But when Peter examined the output from 
  the narrow filters, (the FFT bins)  it lookdd like, and appeared to show 
  itself to be Gaussian.   He said it passed the tests for Gaussian 
  noise
  
  A mathematician could probably prove that any random non Gaussian signal 
  if filtered sufficiently narrow in comparison to itsnature, would end up 
  Gaussian in the filtered bandwidth. 
  
  In fact, to end up non-Gaussian, it would have to have definite 
  components repeating at rates very close to the reciprocal of the bandwidth of 
  the filter.
  
  Andy  G4JNT