The value $ is the highest value assumed by the integrated 

 curve. To find this value, a calibration is made of a pure sinusoid 

 for the "integral of energy" mode of operation. This appears in 

 the lower right-hand corner of Figure 9 . The maximum value of the 

 calibration curve is given by Equation [5] . The maximum value of 

 the cumulative curve is given by 



$ = ii V^ C2 [9] 



Lg P T 



where L^/Lg is the ratio of the height of the seakeeping cumulative 

 curve to the height of the calibration curve. $ is given in sea- 

 keeping units squared. 



3. CONFIDENCE BANDS 



The presentation of the energy spectrum of a seakeeping 

 event would not be complete without some measure of confidence. 

 This confidence is usually expressed by a pair of curves which 

 flank the spectral density curve in such a way that it may be said: 

 "The true spectrum is expected to lie between the two curves with 

 a probability of x." 



The confidence bands are determined from the chi-squared distri- 

 bution with f degrees of freedom where 



f = 2TAf til] 



a 



T is the time it takes the magnetic tape loop to make one traverse 

 through the analyzer. 



The number of degrees of freedom is entered into Figure 10 



24 



