S(w)d(w +m") 
dZ(w) aZ(w') 
, (9.21) 
Sx(@)0(W +’) 
dX(w) dX(w') 
S:(@), S;(@) being the spectrum of wave height €(r) and response x(t), respectively. Here, 
however, for simplicity we use the ordinary Fourier integral form. 
From Eqs. 9.18, 9.19, and 9.13, Eq. 9.11 will be 
os | oA] X(w)e!?"'dw + | Yiodaten)xcanettdeo + | Astorx(o ela 
oO 
= | B(w)Z(w)e' dow. (9.22) 
From Eq. 9.19 
x(t—T) = | X(w)el'e@T dy. (9.23) 
1 
27 
—o 
Then setting 
| Aw )e!@"dw = k,(t) 
-% (9.24) 
| B(w)e?"*dw = I(r), 
Eq. 9.22 will be in the form of a Fourier convolution, 
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