z- ( ). , - , z- z-. , . .
z , - .
:
1. .
2. b(n) a(m) (9.1.3). :
z-.
.
z-.
z-.
3. , / .
4. .
, . ws exp(-jwsDt):
|H(w)| = Ui / Vj, (9.2.1)
zs = exp(-jwsDt) (zs ni) ni -, Ui = |(zs ni)| zs i-, (zs pj) pj- Vj = (zs pj). , . ws ( ). , , ws , , .
:
1. 0 250 .
2. fp = 125 3 Dp =10 .
3. fD = 500 .
500 Dt = 1/fD, fN = 1/2Dt = 250 . , n1 = exp(-j2p 0 Dt) = 1 n2 = exp(-j2p 250 Dt) = -1. z- p 180o . fp/fN = 90o. r ( 0 < r < 1.1) :
|
|
r 1 + (Dp/fD)p. r 1.063.
:
H(z) = (z-1)(z+1) / [(z-r exp(jp/2) (z-r exp(-jp/2)] = (z2 -1)/(z2 +r2) = Y(z)/X(z).
z2Y(z)+r2Y(z) = z2X(z)-X(z). Y(z) = [z2X(z)-X(z)-z2Y(z)] / r2.
:
y(k) = [x(k-2) x(k) y(k-2)] / r2.
z-1 ( r < 1):
r 1 - (Dp/fD)p. r 0.937.
:
H(z) = (z-1)(z+1) / [(z-r exp(jp/2) (z-r exp(-jp/2)] = (z2 -1)/(z2 +r2) = (1-z-2) / (1+r2 z-2).
y(k) = x(k) x(k-2) r2 y(k-2).
. 9.2.1. h1, H1, y1 , h2, H2, y2 ( z-1). , . r fp , 1 fp.
. 9.2.1.
, z 1/z , - . , - p.
z- , , .
H(s) h(t), z-,
, :
H(s) = C / (s-p).
H(s) Dt:
h(t) = TL-1[H(s)] = C exp(pt) → C exp(pnDt).
z- H(z):
H(z) = h(nDt) zn = C exp(pnDt) zn = C / (1-z exp(pDt)).
H(s) , Hi(z), .
z- s- z-:
(s-a) → z exp(aDt).
:
(s-a)(s-a*) → 1 2z exp(Re(a)Dt) cos(Im(a)Dt) + z2 exp(Re(a)Dt).
|
|
, , . .
z- - :
s = g (1-z) / (1+z), g = 1 2/Dt,
jw s- z-, s- , . z-1 :
s = g (z-1) / (z+1).
H(z) H(s). H(z) H(s). ( ∞ wN) . .