PARTI 
A REVIEW OF SPECTRAL ANALYSIS THROUGH PERIODOGRAM 
(NONPARAMETRIC SPECTRAL ANALYSIS) 
To clarify the problems and difficulties encountered in sample computations and 
make them the basis for further discussions, the rough scheme of the techniques of spec- 
trum analysis (through periodograms, the popular nonparametric method) will be 
reviewed first in Chapter 2. Then some ideas proposed by this author for solving these 
difficulties will be summarized in Chapter 3, Part I. Many text books,!*3 especially the 
comprehensive one by Priestley,”3 were used as references in Chapter 2. 
CHAPTER 2 
BASIC PROCEDURE OF THE SPECTRAL ANALYSIS AND 
THE PROBLEM OF SAMPLE COMPUTATIONS 
2.1 RANDOM PROCESS AND ITS CHARACTERISTICS 
Here the general continuous process on f is expressed by X(f), its realization as x(t), 
and the probability density distribution function related to this process as p,(x). The gen- 
eral discrete process is X,, its realization is X;, and probability distribution density function 
is p;(x). Then, as expected values, 
foe) 
mean [X(1)] = E [X(.)] = | x(t)p(x)dx = M(t) (2.1) 
—o 
var. [X()] = E [oo zi ac} | = | L()-BwO!P pixdx = 07(t). (2.2) 
—o 
Usually, the probability density distribution function P(x) is a function of t ; accord- 
ingly, the mean u(r) and the variance o°(t) are also functions of time. 
Joint probability density distribution functions, Prytgty .. .4,(41,%2,X3, . . . Xp) Exist 
for all n,n =1,2,...n,(n—> oo) and all p,,(x1),p,(x2), .. . > Pyn%1%2), ... 65 
Prytyt,(%1,%X2,X3), ...5 .... are defined as their marginal functions. 
