perenne ni Sap (2.62) 
(1.2 to 1.5)w-. 
2.5 COMPUTATION OF THE SPECTRUM FOR A DISCRETE PROCESS 
Here the procedure for calculating the spectrum for a discrete process is summa- 
rized. In many steps of the computations, the finiteness of the sample process, the 
discreteness of the data, and the choice of parameters will affect the results statistically 
and mathematically. 
25.1 Spectrum Computation Through Periodogram 
First, we take the periodogram Py(w) that is the square of the finite Fourier trans- 
form F,(@) of a single realization of this discrete process. 
N 
1 
F,(w) = —— > X, ™, (2.63) 
/2nN 2 : 
1 N 2 
Pn(@) = IF(w)\ — Sse eiwt 
ml t=1 
eel 
a SN, S Xn, X;, cos (t)—t2)o, (2.64) 
4=1 H=1 
setting 
Garat 
t2 > t+r 
1 N-1 1 
am — X, Xiir| COS rw. (2.65) 
2n r=—(N-1) N 
1 
From Eq. 2.24, we know that (=) -X;, Xt4i| 1S the biased estimate of the autocorrelation 
R(r). Therefore, 
1 N-1 
Py@)=— >. RO) cos rw. (2.66) 
r=—(N-1) 
23 
