this shift are best in this analysis and closest to the experimental data obtained in regular 
waves. 
CROSS SPECTRUM 
FT.DEG.SEC 
1 
ROLL-WAVE 
x10~4 (FEET)*-SEC 
SPECTRUM RUN NO. 834 
WITH BK. 
v=0 
SPECTRUM II 
m = 40 0 
m = 60 ° 
— -e — (m= 40, WITHOUT SHIFT) 
—<o— (m = 60, WITH SHIFT 9.47) 
Fig. 3.3. Auto and cross spectra of wave, roll, rolt-wave (run 834) (max. 
lag no. m=60 with shift and m=40 without shift). 
(From Yamanouchi.3") 
3.3. IMPULSE RESPONSE FUNCTIONS FROM THE CROSS 
AND AUTO CORRELATIONS 
By Eq. 2.169 for a linear system, 
We= yy ee Xe: (3.5) 
u=—-@ 
where g,, is the linear impulse response function of the linear system, X, and Y, are the 
input and output, respectively, and N, is the noise, uncorrelated with X,and Y,. By Eq. 
2.164 
70 
