INTRODUCTION 



The study reported here was undertaken to investigate 

 the probability density distribution of the amplitudes of 

 ocean ambient noise and ship noise with respect to various 

 bandwidths in several frequency ranges. The question to 

 be answered was whether ambient noise, without any ship 

 noise or biological noises, can be considered gaussian, and 

 whether the presence of ship noise significantly changes the 

 probability of density distributions. A secondary objective 

 was to investigate methods of data reduction of the probability 

 density curves obtained with the B & K Probability Density 

 Analyzer, using standard statistical tests. 



The probability density function, as treated throughout 

 this report, may be defined as follows. 



Lim , . 



™. ' Ax. a \ 



p(x) = Ax-0 _t I (1) 



N 



N~ CO 



where x is a random variable, with its range of values 

 divided into a large number of continuous intervals Ax. 

 Measure its instantaneous value a great number of times N. 

 Let n. be the number of measured values of x in the tth 

 interval {Ax . ). 



The above equation can be rewritten as 



Lim . , , A 



At . I Ax, ... 



p{x) = Ax-* v i (2) 



T 



T — <n 



where A t . is the amount of time the signal spends in the 

 interval A^ and T is the total time of the sample. Equation 

 2 indicates more clearly how the B & K PDA measures the 

 probability density function. A more detailed explanation 

 can be found in reference 1. (See list of references at end 

 of report. ) 



