(-) . z-.
z-. z- , . , , ( ), :
H(z) = 1-z. (9.3.1)
(9.3.1) n1=1. . 9.3.1, H(w) wi 0 wN=p/Dt - , (9.3.1), Vn1, H(z) - n1 , wi - z(wi) . w = 0 . - , 9.3.2 (9.3.1), -.
. 9.3.1. . . 9.3.2. . |
. , (9.3.1) :
H(z) = G(1-z)/(1-az), zp= 1/a. (9.3.2)
, p1 = 1.01, , =0,99. G H(z) 1 . G=0.995. , Dt=1:
H(z) = 0,995(1-z)/(1-0.99z),
y(k) = 0.995[x(k) x(k-1)]+ 0.99y(k-1).
. 9.3.3. |
n1 1 z- .9.3.1. wi Vn1(z) Vp1(z) z(wi) , :
|H(z)| = G Vn1(z)/Vp1(z).
. 9.3.3 Vn1(z) Vp1(z):
j(w) = jn1-jp1.
. wv z-. :
jv = pwv/wN. (9.3.3)
(9.3.3) , - ( ), ..:
Hv(z) = G(z-zn)(z-zn*)/[(z-zp)(z-zp*)]. (9.3.4)
:
zn = cos jv + j sin jv = Re zn + j Im zn. (9.3.5)
- R:
zp = R cos jv + j R sin jv = Re zp + j Im zp. (9.3.6)
(n2 n2*) (2 2*) .9.3.1. (9.3.5-9.3.6) (9.3.4), :
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Hv(z) = , (9.3.7)
G = [1+(1+2Re zp)/R2] / (2+2Re zn). (9.3.8)
(9.3.7) :
Hv(z) = , (9.3.7')
b0 = 1, b1 = -2Re zn, b2 = 1. (9.3.9)
a1 = - (2Re zp)/R2, a2 = 1/R2.
, :
y(k) = G[x(k) +b1x(k-1)+x(k-2)] a1y(k-1) a2y(k-2). (9.3.10)
. fs = 50 , . Dt = 0.001 .
: fN = 1/2Dt = 500 .
z-: j = pfs/fN = 0.1π.
R = 1.01. :
zn = cos j + j sin j = 0.951 + 0.309 j, zp = Rcos jv + j Rsin jv = 0.961 + 0.312 j.
G (9.3.8): G = 0.99.
: b1 = -2Re zn = -1.902,
a1 = - (2Re zp)/R2 = -1.883, a2 = 1/R2 = 0.98.
(9.3.7') z = exp(-jω):
H(w) = 0.99[1-1.902exp(-jω)+exp(-2jω)] / [1-1.883exp(-jω)+0.98exp(-2jω)].
: y(k) = 0.99[x(k) - 1.902 x(k-1) + x(k-2)] + 1.883 y(k-1) 0.98 y(k-2).
. 9.3.4 , 50 53 , ( ). . , . 50 .
. 9.3.4.
. 9.3.5. |
R → 1 , , , . (4÷5)/(R-1). , , . 9.3.5. . ( ), G.
. (9.3.4) , , ωs , :
Hs(z) = G/[(z-zp)(z-zp*)] = G1/(1+a1z+a2z2). (9.3.11)
. 9.3.6. |
(9.3.11) z- (. 9.3.1). (, 2 2*) ω . ω π ( z- ) ( ) ( 2), ( ) , ω ( ωs), . , Hs(ω) ωs R → 1 . . 9.3.6.
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1 G1 Hs(ω) = 1 ω = ωs, ..:
G1 = 1+a1 z(ws)+a2 z(ws)2.
. 9.3.7. |
(9.3.11) . , Hv(z):
Hs(z) = 1-Hv(z).
Hs(z) = . (9.3.12)
0 = 1-G, c1 = a1-Gb1, c2 = a2-G.
. 9.3.7. , , . 9.3.8.
. 9.3.8. . |
11-07. - .
12-07. .
13-07. .
14-07. .