Wave Height Reference 



Fig. 2 - Wave height defined as an input signal 



example, in defining a linear system in the time domain it is conventional to use 

 a unit impulse as a standard input, which causes an "impulse response" whose 

 Fourier transform is identical to the frequency response function. This is seen 

 from Eq. (2), where 



Y(ico) = G(ja;) 



because the transform X( jco) of a unit impulse is unity. 



(4) 



Since it is impossible for a physical system to look into the future, to "laugh 

 before it's tickled," the impulse response must be zero prior to t = (when 

 the impulse arrives). However, in the ship motion problem there is no reason 

 to believe that the inverse transform of an experimental frequency response will 

 exist only in positive time. In fact, as will be shown later in this report, an 

 "impulse" of wave height observed at t = at the center of gravity of the model 

 would be caused by the contraction of a wave train, which had previously passed 

 along the forward part of the ship, producing force on the hull and resultant mo- 

 tion in negative time. Thus, a more accurate description of the phenomena in- 

 volved would be the very general configuration pictured in Fig. 3, where uni- 

 directional wave height and ship motion are both viewed as responses to some 

 undefined initial excitation, the mechanism which produces the waves. However, 

 since wave height and ship motion are completely related in the sense that they 

 respond to the single cause, it is proper to consider that ship motion can be re- 

 lated to wave height by the frequency relation 



WAVE HEIGHT 

 x(t) 



SHIP MOTION 

 y{t) 



Fig. 3 - Representation of wave height and ship mo- 

 tion as "effects" rather than "cause" and "effect" 



510 



