DYER: FLUCTUATIONS: AN OVERVIEW 



The time series, A(t), has a probability density, P{A), and a 

 spread, AA(Q) called the fading range. This can be defined in terms 

 of the cumulative probability distribution, and in the subsequent 

 results it will correspond to the fading range where 2.5 percent of 

 the lowest levels and 2.5 percent of the highest levels are dis- 

 carded. 



Similarly, a period, T. , can be defined as the time between 

 crossings of a level A going in the same direction. The period is, 

 in fact, a function of that level. 



The crossing period T is therefore related to the crossing 

 rate T.~-^ which is given by the integral of the absolute magnitude 

 of the slope of the curve times the joint probability density of 

 that particular level which it crosses and the slope itself. In the 

 subsequent results, the periods will correspond to the crossing level 

 that is the mean of the time series. In case of phase, for example, 

 that mean will often be zero. 



A third measure, the autocorrelation, p, is defined in the usual 

 way, and the time, i, will correspond to the 1/e point on that auto- 

 correlation function. 



Figure 2 summarizes some of the knowledge acquired by those 

 working on the Eleuthera-Bermuda experiment. There are several 

 fading types. The very fast fading type extends from an averaging 

 time of perhaps ten times the period of the sound wave itself up to 

 approximately 15 seconds. A fading in this domain of averaging time 

 and record time — that is, the length of time we look at a record — 

 is usually incorporated within scattering theories and scattering 

 experiments. 



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