Figure B-5 Illustrates the performance of the province picker when 

 white noise Is Input. Examination of this output results in some inter- 

 esting insights into the nature of stochastic processes. Despite the 

 known property that the input signal has a perfectly flat, non-variable 

 amplitude spectrum, all ten band-pass filtered signals show large fluc- 

 tuations in amplitude. The amplitude recorded in the frequency spectrum 

 represents simply an average amplitude computed over the length of the 

 input time series. At any discrete point, the amplitude at a frequency 

 could be widely removed from the average value. It was discovered 

 through experimentation that these fluctuations were damped when wider 

 band-pass filters were used; thus, the overlapping filter bank illus- 

 trated in Figure B-1 was designed. The slope values (plotted above the 

 ten band-passed signals) do fluctuate about zero as expected. The 

 standard deviation about zero averages about 0.2 over several runs which 

 implies (assuming a no-Tnal distribution) that a change of olope of -0.4 

 can be detected with 95% confidence. Many of the decisions made In gen- 

 erating the regression analysis and smoothing, were designed to minimize 

 this fluctuation. 



In order to design a province detector properly, it is necessary to 

 combine known signals of differing spectral slopes and RMS energies. 

 For the purpose of this study, the resulting signal must also have an 

 amplitude spectrum with power law form. One method of generating such a 

 signal is through a Markov chain with a probability transition matrix 

 which allows subsequent events either to raise or lower a constant 

 Increment with probability of 0.5 (see Ross, 1980). This signal, which 

 is a special case of a random walk, fluctuates about its initial value 

 and has a spectral form of 



143 



