10/:
- , - .
. , XIX .
. . . , .
. , XX .
: 10.1. . . . . 10.2. . . . . . .
, . .
[1,25].
. . , ,
u(t) = Uo cos (wot+j)
:
, , .
, s(t), ( , ) S(w). S(w) s(t) , t = 0, . . 10.1.1 (), () ().
. 10.1.1. , , .
. - :
s(t) = S(w)exp(jwt) dw + S(w)exp(jwt) dw. (10.1.1)
. s(t) ( ), ( ) S(w). , s(t), (10.1.1), p, .. s(t) :
zs(t) = . (10.1.2)
, zs(t), , :
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zs(t) = Re z(t) + jIm z(t).
(10.1.1) zs*(t), z(t):
zs*(t) = Re z(t) - jIm z(t),
. 10.1.2 , . 10.1.1-.
. 10.1.2. z(t) z*(t).
zs(t) zs*(t) (10.1.2) 1/π, 1/2π, (10.1.1), s(t):
s(t) = [zs(t)+zs*(t)]/2 = Re z(t).
, zs(t) s(t).
. , , 1/pf. , zs(t) Re z(t) = s(t) , s(t):
Im(z(t)) = = TH[s(t)] = s(t) * hb(t), (10.1.3)
hb(t) = 1/(πt),
zs(t) = s(t) + j× . (10.1.4)
, s(t), hb(t) .
, s(t) s(t) 1/(πt) :
= , (10.1.3')
, . , , s(t). - , .
? ? .
, , :
Zs(w) = zs(t) exp(-jwt) dt.
, (10.1.2), , ( p, 2p) s(t):
Zs(w) = (10.1.5)
, (10.1.4) zs(t), :
Zs(w) = S(w) + j . (10.1.6)
( -¥ +¥) (10.1.5). , ( w) (10.1.6) , . .
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. 10.1.3.
S(w) -1, w=0 , , . 10.1.3), S(w) 2 . S(w) sgn(w):
sgn(w) = (10.1.7)
sgn(w)S(w), . 10.1.3, , , . j. wl wr, :
S(w) = Re S(wl) + jIm(wl) + Re S(wr) + jIm(wr),
= jRe S(wl) - Im(wl) - jRe S(wr) + Im(wr).
j ( (10.1.6)):
j = -Re S(wl) - jIm(wl) + Re S(wr) + jIm(wr).
:
Zs(w) = S(w) + j = = 2Re S(wr) + j2Im(wr) = 2S(wr),
(10.1.5). :
= = -j×sgn(w)×S(w), (10.1.8)
Hb(w) = -j×sgn(w) = (10.1.9)
, S(w) s(t) -j×sgn(w). S(w) + j .
. 10.1.4. |
(10.1.8) s(t) :
= s(t) * hb(t), (10.1.10)
s(t) = - * hb(t). (10.1.11)
hb(t) = TF[-j×sgn(w)] = 1/(pt) -j×sgn(w).
x(t) zx(t) = x(t) + j . 10.1.4.
(10.1.9) :
Hb(w) = |Hb(w)|×exp(jjh(w)), |Hb(w)| = 1.
Hb(w) = -j×sgn(w) = , (10.1.12)
x(t)
S(w) = |S(w)|×exp(jjs(w)),
(10.1.8) :
= |S(w)|×exp(jjs(w))×exp(jjh(w)) = |S(w)|×exp[j(js(w)+jh(w))], (10.1.8')
.. |S(w)| - s(t), s(t). ( ) -90 w > 0 90 w < 0 s(t). , , . . , x(t) = cos(2pfot), :
(t) = TH[x(t)] Û TF[TH[x(t)]] = -j sgn(f)×[d(f+fo)+d(f-fo)]/2.
(f) = -j×[-d(f+fo)+d(f-fo)]/2 = j[d(f+fo)-d(f-fo)]/2.
- . :
(t) = TF-1[ (f)] = sin(2pfot).
. 10.1.5. |
x(t) = sin(2pfot) (t) = -cos(2pfot). () , , . . . 10.1.5 ( ) .
, , , , 900 .
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