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Figure 2 - Frequency Response of Actuator Wavemaking System as Determined 

 from Sinusoidal Excitation 



It is well known that the amplitude spectrum of a random process is multiplied by the 

 square of the magnitude of the frequency response of a linear system through which the 

 process passes. It was reasoned that if the voltage applied to the actuators had a power 

 density spectrum with the desired Neumann shape, multiplied by a term inversely proportional 

 to the square of the frequency response of the wavemaking system, the resulting wave height 

 observed in the water would have the desired Neumann weighting. In other words, the charac- 

 teristics of the wavemakers would be effectively cancelled out with the excitation signal. 



The problem then becomes the generation and recording of a random voltage with the 

 desired power density spectrum, i.e., the Neumann shape times the inverse wavemaker char- 

 acteristics. Fortunately, this is a well-established technique in analog computer simulation 

 developed for use in statistical studies of complex systems. 



The standard source of randomness in the analog computation facility is the so-called 

 "white noise" generator which produces a random signal with a relatively flat power spectral 

 density over a large frequency range and which has the desired Gaussian characteristics. 

 The steps in programming are: 



1. A random noise source is used to excite a properly designed linear system on the 

 analog computer, and the output of this system is recorded on magnetic tape. 



2. This signal on magnetic tape is used to control all wavemaking systems in unison, 

 creating a unidirectional random wave pattern. 



