or directly by multiplying Equation [ 3 ] by 2 it . 



The ordinate scale of the spectrum representation requires 

 attention next. Where the local oscillator scale was used to represent 

 the analysis frequency scale, the peak voltage output of a pure 

 sinusoid is used to represent one point on the analysis ordinate scale. 

 This calibration factor is obtained by analyzing a pure sinusoid 

 in the same way (same constants) as the particular seakeeping event 

 being analyzed. Since the bandwidth of the filter is much greater 

 than the frequency band of the calibration signal (zero), the result 

 is a curve which represents the characteristics of the filter rather 

 than the pure sinusoid. This is all right because only the peak value 

 of this curve is important, at the moment. Figure 7 shows typical 

 calibration curves for different filters. According to our analysis 

 technique, the peak value of the calibration curve is the square of 

 the amplitude of the pure sinusoid being analyzed. If this amplitude 



is characterized by its rms (root -mean- square) voltage input (V ), 



2 

 then the peak value of the resulting calibration curve (V ) is 



V^ = (n/2V )2 = 2V (volts^) [5] 

 p rms ms "■ ^ 



Figure 8 shows a spectral density analysis of a seakeeping 

 variable made with a 5-cps filter. The calibration curve appears 

 at the right. Since the rms input voltage is V -0.04, the output 

 peak value is by Equation [5] , V^ = 0.0031 volts^. This is the 



20 



