Understanding and Prediction of Ship Motions 



•' - CO 



-[ 



h(T- ^) R^^Cm) d^ 



This corresponds to 



SyxC'^) = «(«) -SxxC^) 



Namely Ry^C^") is connected with R^xC^) by the impulse response function h(T) 

 just as y(t) with x(t). As is very clear, the relation between Ry^C^) ^'^dRxx^^'^) 

 is much stabler from the statistical point of view than that between y(t) and 



x(t). 



When the computation is carried out digitally from the sample of data taken 

 at interval At, 



Ryx(^) = ^ »1(M) RxxC-^- t) At . 



Putting At as 1 for the purpose of simplification 



RyxC-^) = 2 h(/X) Rxx(-^-/^) • 



The impulse response can be obtained discretely as the form of a weight func- 

 tion, for example as h_^, h,^^j, . . . h^, . . . h^ j, h^, by solving the simulta- 

 neous equations 



Ryx^-") 



Ryx(-n+ 1) 



Ryx(O) 



Rvv(n-l) 



Rvx(n) 



Kxx(O) 

 Rxx(l) 



Rxx(n) 



Rxx(l) •••RxxC") •••RxxC2n) 



RxxCO) ...Rxx(n-l)...Rxx(2n-l) 



R rn-1) ...R_CO) 



•Rxx(") 



Rxx(2n-1) R,,(2n-2)...R,/n-l)...R^^(l) 

 RxxC2n) R,,C2n-l)...R^^(n) ...Rxx(O) 



Figure 15 shows the impulse response function obtained by solving a 59th order 

 simultaneous equations from Ry^ at r = -29 -- +29 and R^^ at r = - 58 of roll 

 and wave height correlation, shown in Fig. 7. In the same figure, the impulse 

 response function, calculated as the Fourier inversion of H(a)) that was obtained 

 through the spectrum analysis as in Fig. 14, is drawn. The latter was calculated 

 as h gj, ~ hgp, and the figure shows the main part of it. The two weight fvinctions 

 are not necessarily the same. To our surprise, however, inversely, the frequency 



221-249 O - 66 



113 



