and Prof. W. J. Pierson Jr.4 in 1953. We had to start on our Own independent of the 
achievements in the USA. 
1.2 PURSUING THE IMPROVEMENT OF COHERENCY FUNCTIONS 
After the bases for the mathematical and statistical theories were established by N. 
Wiener,>-° J. L. Doob,’ C. E. Shannon, §, O. Rice,’ and others, mostly in the 1940’s, the 
stochastic analysis techniques were applied in many scientific and engineering fields 
besides communications and control engineering. These techniques were adopted rather 
early in the analysis of ocean waves and of a ship’s response at sea. This method has been 
pretty well formulated by the efforts of oceanographers like G. Neumann,!° W. J. Pierson, 
Jr.,! M. S. Longuet-Higgins,!2 D. E. Cartwright and M. S. Longuet—Higgins,!3 and by 
the pioneering work of M. St. Denis and W. J. Pierson, Jr.,4 succeeded by E. V. Lewis,!4 
and J. F. Dalzell and Y. Yamanouchi,!5 and is now rather popular with us. We now know 
that, in practical applications and when applying certain theories, a few statistical consid- 
erations are necessary in the numerical computations in order to get reliable results. 
In Part I, the author tried to show the problems encountered in sample computa- 
tions, in the so—called correlation method that are also closely related to the basis for 
model fitting techniques (that is, the parametric method treated in Part II) and reviews the 
conventional nonparametric method. The author did not intend to go into detail about the 
analysis technique. 
The coherency function, if properly calculated, is a good index of the extent to 
which spectrum analysis, as a linear process, is valid for application to a stochastic pro- 
cess. A few results of this author’s efforts in this field, presented later in Part I, are related 
to improvement of the techniques for obtaining a good estimate of coherencies. 
1.3 TIME DOMAIN CHARACTERISTICS 
Time series analysis is sometimes called spectrum analysis, thus showing that esti- 
mation of reliable spectral functions is very important in the analysis of time series. 
Spectral functions are surely powerful functions which provide good information on 
a stochastic process and also resolve the tangled relations of convoluted types in the time 
domain. However, because of this fact, and also partly because (auto) correlation did not 
appear in an important way, in St. Denis and Pierson’s pioneering paper,’ rather little at- 
tention has been paid by naval architects to the time domain relations over the past few 
decades. From his first involvement in this study, this author has thought that time do- 
main functions deserved more attention and has made some efforts along this line. 
Of course spectral functions and correlation functions are actually the same function 
expressed in different ways. Sometimes, however, in sample computations, applying the 
time domain expression helps us understand the characteristics of the stochastic process 
better, because we are accustomed to expressing the physical process by differential equa- 
tions that are expressions in the time domain. The time domain expression of stochastic 
processes helps us in the analysis to use already known characteristics of the process. 
Moreover, the correlation window Operation in the sample computation is just a multiply- 
ing operation, whereas the spectral window operation is now an entangled convolution 
operation that is more complex in real sample computations. In sample computations, 
