1 a TS 
P(21, 22) = ——7==— ex ESE ip ae 
2at Jokes >| 2kag 2) 
A 
omy | actu ae 2 
Vk} 6 koavkon ~ \ Vkoo 
an| 
a 
S a] 
tom 
a 
ki0 Z1 
x |H5+—— H, | — ] + 
€ kip Zi 22 
+— H, | — | @, | —— ]]. (2.113) 
Here H,,, (x) is a Hermite polynomial, 
1 Up ; 
H,(x)=—= +i/20)"dt 
(x) iE Je (x+1V2t) 
H (x)= 1 
Hy (x)=x 
Hy(x)=x-1 
H3(x) =x -3x 
A n+) (&) = XH, (x) — nH) (x) (12.114) 
convention of (0) is omitted. 
Under the assumption that z,(r) is narrow banded, the number of zero—crossings of 
an output z(f) is equal to the number of maxima. 
Therefore, the expected number of z—up crossings per unit time is given as already 
shown in Section 12.5, Eq. 12.44, 
E[N,(z1)] = | lzo| p(z1, 22)d22. (12.115) 
N]e 
358 
