. , . ( , single side band - SSB) 5.1.11. ( '+' ) ( '-') :
u(t) = Umcos(wot+jo) + (Um/2) Mncos[(woWn)t+jo Fn]. (5.2.3)
. 5.10. .
, . 5.10 , , , , U(t), = 1 ( ).
, , , . 2 .
( , -), .
, , , . .
s1(t) s2(t) ( ) . . . 5.11, s1 s2.
. 5.11. .
- . , :
smono(t) = s1(t) + s2(t), sdiff(t)= s1(t) - s2(t),
:
s1(t) = (smono(t)+sdiff(t))/2, s1(t) = (smono(t) - sdiff(t))/2.
, . wo (subcarrier), ( ), ( ):
s(t) = smono(t) + (Ao + sdiff(t))cos(wot).
. , , . . 5.11, , . . 0, , .
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(angle modulation) u(t) = Umcos(wt+j) Um , s(t) w, j. , u(t) y(t) = wt+j, .
(, phase modulation - PM). wo s(t). , :
u(t) = Um cos[wot + k×s(t)]
k . . 5.12
. 5.12. .
s(t) = 0, uo(t). s(t) y(t)=wot+k×s(t) wot. , s(t) . s(t) Dy wot ( Dj = k×smax(t), Dj = k×smin(t) ).
(instantaneous frequency), :
ω(t) = y(t)/dt = ωo + k ds(t)/dt.
:
y(t) = ω(t) dt, y(t) = ω(t) dt +jo.
(, frequency modulation - FM) , wo :
w(t) = wo + k×s(t)
, :
y(t) = ωo(t) + k s(t) dt, y(t) = ωo(t) + k s(t) dt +jo.
:
u(t) = Um cos(ωot+k s(t) dt +jo)
, Dw = k×smax(t), Dw = k×smin(t).
. , , . (). , , , s(t) .
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. ω. :
j(t) = b sin(Wt),
b - (modulation index), . ω:
y(t) = wot + b sin(Wt).
:
u(t) = Um cos(wot + b sin(Wt))
:
ω(t) = dy(t)/dt = wo + bW cos(Wt).
, , . ω ωd = bW, (frequency deviation). , :
b = ωd/W.
W .
W, :
b = const, ωd = b W.
, , :
ωd = const, b = ωd/W.
.
(9.2.4) :
u(t) = Umcos(b×sin(Wt)) cos(wot) - Umsin(b×sin(Wt)) sin(wot).
(b<<1, ) :
cos(b×sin(Wt)) 1, sin(b×sin(Wt)) b×sin(wot).
(9.2.6), :
u(t) Umcos(wot) + (bUm/2)cos[(wo+W)t] + (-bUm/2)cos[(wo-W)t
(9.1.4) , b<<1 wo+W wo-W. , .. 1800 . , 180 . , b .
5.13 .
b :
u(t)=Um Jk(m) cos[(wo+kW)t],
Jk(m) k- m=b. , - , wokW, , , Jk(m). Um=1 . 5.13
b . b , . , ω . . 5.13 , (2.405, 5.52, 8.654 ..) wo . . 5.14.
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, , . :
= 2(b+1)W,
.. k>(b+1) . , , b>>1, :
2bW = 2wd
5.14 .
( 2500 , 25 , )
, , 2W, , b . , .
: J-k(m) = (-1)kJk(m). , wo+kW wo-kW k, 180 k.
. , woW1W2...Wi, Wi. .
, . - :
s(t) = u(t) cos(ωot+j(t)).
s(t) , . -.
s(t) = u(t) cos(ωot) cos j(t) u(t) sin(ωot) sin j(t).
a(t) = u(t) cos j(t) b(t) = -u(t) sin j(t), a(t) b(t) cos(ωot) sin(ωot), 90 :
s(t) = a(t) cos(ωot) + b(t) sin(ωot).
(quadrature), - ().
(9.1.17) :
S(ω) = ½ A(ω+ωo) + ½ A(ω-ωo) ½j B(ω+ωo) + ½j B(ω-ωo).
, 90:
s1(t) = s(t) cos ωot = ½ a(t) + ½ a(t) cos 2ωot + ½ b(t) sin 2ωot,
s2(t) = s(t) sin ωot = ½ b(t) + ½ a(t) sin 2ωot - ½ b(t) cos 2ωot.
a(t) b(t) . , .