Understanding and Prediction of Ship Motions 



damping a/co = y is very large and H(a>) does not decay so much at 3oj^, that a 

 small peak will appear around 3^^, when the velocity square damping exists. 



NOMENCLATURE 



o) circular frequency = 2-ni, f = frequency, 



t time, 



At time interval between adjacent data values (sampling time interval), 



x(t) input to the system, assumed to be a weakly stationary stochastic 

 process, 



y( t ) output of the system, under the input x( t ) and usually contaminated 

 with noise n(t), 



x(n) x(nAt), 

 y(t) y(nAt), 



H(aj) frequency response function of the system, when the system is 

 linear and time-invariant; otherwise, that of the corresponding 

 linearized system, 



I HC oj) I amplitude gain, 



cr(cS) Arg {H(aj)}, phase shift defined by H(a)) = |H(aj) | exp {jcr(aj)} (j 2 = -i)j 



h( r) impulse response function of the system when the system is linear 

 and time-invariant, 



m maximum number of lags of correlation computed, T^ = mAt , 



N number of data used, NAt = total length of observation, 



R( t) covariance function, 



S(oS) power spectrum function. 



REFERENCES 



1. Blackmann, R. B. and Tukey, John W., "The measurement of power spectra 

 from the point of view of communications engineering," Part I and II, Bell 

 System Tech. Jour., Vol. XXXVII, No. 1, Jan. 1958 and No. 2, March 1958. 



2. Akaike, Hirotugu; Yamanouchi, Yasufumi; Kawashima, Rihei and others: 

 "Studies on the statistical estimation of frequency response function," An- 

 nals of the Institute of Statistical Mathematics Supplement III, 1964. 



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