The relationship shows that, if we assume the asymptotic normality of the spectrum 
estimate, then the proportional error 6(w) can be estimated from the equivalent number of 
degrees of freedom of the spectrum estimation v, by Eq. 2.113, p and c(p) being the level 
of confidence and p/100 the point of normal distribution as 
c(@) 2 
| wieder (2.114) 
—c(@) 
From Eq. 2.98 or Table 2.2, we know that v is proportional to N/M, and for most of 
the windows 2 to 3 times N/M. If, for example, N/M = 10 to 15, then v is on the order 
of v = 30. If we adopt the confidence level of p = 0.95 (95%), then c(p) = 1.96. From 
the appropriate normal distribution 
6(w) = 1.96 2/30 = 0.506. 
This value means that the estimate of the spectrum ordinate has a proportional error in the 
order of 50% for this example. 
25.6 Choice of the Spectral Window 
It is now clear that, in order to get a consistent estimate of s(w), we have to use a 
spectral window. Several spectral windows and their effects on the estimation are summa- 
rized in Table 2.2, from Priestley.”* 
42 
