. z- :
z = exp(-pDt), (9.4.1)
Dt - , p , = s+jw.
(9.4.1) ln z = -pDt ln z :
ln z = -2[(1-z)/(1+z)+(1-z)3/(3(1-z)3)+....], z > 0.
z- :
p = (2/Dt)(1-z)/(1+z). (9.4.2)
, p- z-, . :
p = g(1-z)/(1+z), (9.4.3)
z = (g-p)/(g+p). (9.4.4)
g , g = 1. p = jw (9.4.4) z :
z = r exp(jj(w)), r = |z| = 1.
j(w) = 2 arctg(w/g),
:
w = 0, z = exp(j0) = 1,
w = ¥, z = exp( jp) = -1
. 9.4.1. |
w - ¥ ¥ j(w) -p p (. . 9.4.1), .. p- (p = jw, -¥ < w < ¥) z-, s- , .
. ( ) - ω -¥ +¥. z- : - ¥ ¥ - -p/Dt p/Dt z-. , z-. (9.4.2) z = exp(-jwDt) exp(jwDt/2), :
p = (2/Dt)[exp(jwDt/2)-exp(-jwDt/2)] / [exp(jwDt/2)+exp(-jwDt/2)],
p = (2/Dt) th(jwDt/2). (9.4.5)
- w () , p = jw, th(x) = - jtg(jx), :
w = (2/Dt) tg(wDt/2) = g tg(wDt/2), -p/Dt<w<p/Dt. (9.4.6)
. 9.4.2. . |
(9.4.6) w , , w p-, , , w -¥ ¥, . . 9.4.2 ( p ).