eec4-4a-ss-lecture-08.pdf
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Signals & Systems FEEE, HCMUT
Ch-4: Biu din tn hiu dng bin i Fourier
Lecture-8
4.4. Bin i Fourier v h thng LTI
4.5. B lc l tng v thc t
4.6. ng dng trong thng tin: iu ch lin tc
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Signals & Systems FEEE, HCMUT
4.4. Bin i Fourier v h thng LTI
Xt h thng LTI vi p ng xung l h(t)
Ta c: y(t)=f(t) h(t) Y()=F()H()
Biu din h thng trong min tn s:
H thng ghp lin tng:
1 2Y()=F()H ()H ()
jtY()H()= h(t)e dtF()
(p ng tn s ca HT LTI)
1 2H()=H ()H ()
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Signals & Systems FEEE, HCMUT
4.4. Bin i Fourier v h thng LTI
H thng ghp song song:
1 2Y()=F()[H ()+H ()]
H thng ghp hi tip:
1
1 2
H ()Y()=F()
1+H ()H ()
1 2H()=H ()+H ()
1
1 2
H ()H()=
1+H ()H ()
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Signals & Systems FEEE, HCMUT
4.4. Bin i Fourier v h thng LTI
H thng LTI nhn qu n nh m t bi phng trnh vi phn:
Q(D)y(t)=P(D)f(t)
k kD y(t) ( j) Y()
k kD f(t) ( j) F()
Q(j)Y()=P(j)F()
Y() P(j)H()=
F() Q(j)
V d: xc nh p ng xung ca h thng m t bi PTVP:
(D+3)y(t)=Df(t)
P(j) jH()=
Q(j) j+3C:
31
j+33th(t) (t) 3e u(t)
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Signals & Systems FEEE, HCMUT
4.4. Bin i Fourier v h thng LTI
nh hng ca p ng tn s ca h thng ln tn hiu:
Y()=F()H()|Y()|=|F()||H()|
Y()= F()+ H()
H thng LTI lm thay i bin & pha ca tn hiu vo to tn
hiu ra. Cc thnh phn tn s khc nhau s thay i khc nhau
H thng LTI l mt b chn lc tn s - Filter
B lc thng thp (Low pass Filter LPF)
B lc thng cao (High pass Filter HPF)
B lc thng di (Band pass Filter BPF)
B lc chn di (Band Stop Filter BSF)
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Signals & Systems FEEE, HCMUT
4.5. B lc l tng v thc t
B lc thng thp l tng:
c
2
H()=rect( ) cc
h(t)= sinc( t)
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Signals & Systems FEEE, HCMUT
4.5. B lc l tng v thc t
B lc thng cao l tng:
c
2
H()=1 rect( ) cc
h(t)=(t) sinc( t)
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Signals & Systems FEEE, HCMUT
4.5. B lc l tng v thc t
B lc thng di l tng:
0 0
c2 c1 c2 c1
+
H()=rect( )+rect( )
c2 c1( )c2 c102
h(t)= sinc[ t]cos t
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Signals & Systems FEEE, HCMUT
4.5. B lc l tng v thc t
Nhn xt: cc b lc l tng u l h thng khng nhn qu
khng th thc hin c trn thc t
B lc thc t phi l h thng nhn qu v c thc hin theo
cc phng n sau:
Thc hin bng h thng ri rc (b lc s - s hc trong mn x
l TH s), s dng p ng xung h(t) ca b lc l tng ct b
phn ui ca h(t) v tr i ph hp h(t) mi l nhn qu
Thc hin bng h thng lin tc (b lc tng t), p ng tn
s thay i lin tc tin gn ti p ng l tng (s trnh by
chi tit hn trong chng 7 v thit k b lc tng t)
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Signals & Systems FEEE, HCMUT
4.5. B lc l tng v thc t
Vic ct b h(t) c thc hin bng cc hm ca s. Ty vo loi
hm ca s m p ng tn s ca h thng s c s thay i khc
nhau so vi p ng l tng
tR T
w (t)=rect
tT T
w (t)=
R Rh (t)=h(t)w (t)
T Th (t)=h(t)w (t)
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Signals & Systems FEEE, HCMUT
4.5. B lc l tng v thc t
Mt s hm ca s v c tnh ca chng
Window w(t) Mainlobe
Width
Rolloff
Rate
dB/oct
Peak
Sidelobe
Level dB
1. Rectangular: tT
rect
2. Bartlett: tT
3. Hanning: 2tT
0.5[1 cos ]
4. Hamming: 2tT
0.54 0.46cos
5. Blackman: 2t 4tT T
0.42 0.5cos 0.08cos
6. Kaiser:
2tT0
0
I [ 1 4 ];1 10
I ()
4/T 6 13.3
8/T 12 26.5
8/T
8/T
18
6
31.5
42.7
12/T 18 58.1
11.2/T 6 59.9
( 8.168)
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Signals & Systems FEEE, HCMUT
4.6. ng dng trong thng tin: iu ch lin tc
4.6.1. Gii thiu
4.6.2. iu ch bin (AM)
4.6.3. iu ch gc (PM, FM)
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Signals & Systems FEEE, HCMUT
4.6.1. Gii thiu
iu ch : dch ph tn s ca tn hiu tin tc ln tn s cao hn
Mc ch:
Ghp knh theo tn s
Tha mn nguyn l bc x in t khi truyn v tuyn
Thnh phn trong tn hiu iu ch:
Tn hiu sng mang
Tn hiu bng gc (tn hiu mang thng tin)
Cc loi iu ch:
iu ch bin (AM)
iu ch gc: FM, PM
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Signals & Systems FEEE, HCMUT
4.6.2. iu ch bin (AM)
a) iu ch/gii iu ch AM-DSB-SC
b) Gii iu ch/gii iu ch AM
c) Ghp knh/phn knh theo tn s (FDM)
d) iu ch/gii iu ch AM-SSB
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Signals & Systems FEEE, HCMUT
a) iu ch/gii iu ch AM-DSB-SC
S h thng iu ch:
AM cy (t)=m(t)cos t Tn hiu iu ch:
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Signals & Systems FEEE, HCMUT
a) iu ch/gii iu ch AM-DSB-SC
Ph ca tn hiu iu ch: 1 12 2AM c cY ()= M( )+ M( )
c M
Ph ca tn hiu iu ch cha c 2 di bn LSB & USB v khng
cha thnh phn sng mang nn c gi l iu bin 2 di bn trit
sng mang (AM-DSB-SC)
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Signals & Systems FEEE, HCMUT
a) iu ch/gii iu ch AM-DSB-SC
H thng gii iu ch:
Yu cu: ng b sng mang my pht v my thu T/sng ng b
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Signals & Systems FEEE, HCMUT
b) iu ch/gii iu ch AM
H thng iu ch: nh AM-DSB-SC nhng cng thm sng mang
pm= : modulation index
K
Tn hiu iu ch:
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Signals & Systems FEEE, HCMUT
b) iu ch/gii iu ch AM
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Signals & Systems FEEE, HCMUT
b) iu ch/gii iu ch AM
Ph ca tn hiu iu ch:
1 12 2AM c c c cY () K(- )+K(+ )+ M(- )+ M(+ )
H thng gii iu ch:
Tch sng ng b: tng t nh AM-DSB-SC
Tch sng khng ng b hoc tch sng ng bao
Ging ph tn hiu AM-DSB-SC nhng c thm sng mang nn
c hiu sut thp hn v mt cng sut.
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Signals & Systems FEEE, HCMUT
Tch sng khng ng b:
1
c>> M: lun tha trn thc t (500KHz-2MHz)
b) iu ch/gii iu ch AM
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Signals & Systems FEEE, HCMUT
Ghp knh: cc tn hiu mang tin (cc knh) c cng bng thng,
khi truyn trn mt knh chung s phn bit bi tn s sng mang
Frequency-Division Multiplexing (FDM)
c) Ghp knh/phn knh theo tn s (FDM)
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Signals & Systems FEEE, HCMUT
c) Ghp knh/phn knh theo tn s (FDM)
Ph ca tn hiu FDM:
Phn knh theo tn s:
Thc t ngi ta dng phng php i tn phn knh v gii iu
ch ti cng 1 tn s (thng gi l trung tn)
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Signals & Systems FEEE, HCMUT
d) iu ch/gii iu ch AM-SSB
Xt tn hiu FDM:
USBLSB
USBLSB
Mi knh u c 2 di bn nn chim dng bng thng knh truyn
gp i bng thng ca tin hiu.
Vi cch gii iu ch kho st ta thy rng ch cn truyn i di
cao USB hoc LSB th vn c th gii iu ch c
Nu truyn i mt di bn ca tn hiu ngi ta gi l iu bin
AM mt di bn. Mc ch: tit kim bng thng ca knh truyn
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Signals & Systems FEEE, HCMUT
Phng php iu ch 1: iu ch AM-DSB + Filter
H()
d) iu ch/gii iu ch AM-SSB
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Signals & Systems FEEE, HCMUT
Phng php iu ch 2: 900 phase-shift network
d) iu ch/gii iu ch AM-SSB
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Signals & Systems FEEE, HCMUT
4.6.3 iu ch gc (PM, FM)
a) Nguyn tc iu ch gc
b) Bng thng ca tn hiu iu ch gc
c) Phng php iu ch/gii iu ch gc
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Signals & Systems FEEE, HCMUT
a) Nguyn tc iu ch gc
Nguyn tc: gn tn hiu tin tc m(t) vo gc pha (t) ca sng mang
y (t)=Acos[(t)] (t)=[m(t)]vi
Tn s tc thi: it
(t) d(t) = lim
t dt0
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Signals & Systems FEEE, HCMUT
iu ch FM: tn s tc thi t l tuyn tnh theo m(t)
i c f = +k m(t)t
c f(t)= t+k m()d
iu ch PM: pha tc thi t l tuyn tnh theo m(t)
c p(t)= t+k m(t) i c pdm(t)
= +kdt
Quan h gia FM & PM:
a) Nguyn tc iu ch gc
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Signals & Systems FEEE, HCMUT
V d v tn hiu iu ch PM & FM
a) Nguyn tc iu ch gc
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Signals & Systems FEEE, HCMUT
b) Bng thng ca tn hiu iu ch gc
Quan h ph tn hiu iu ch vi tn hiu tin tc khng n gin
khng xt chi tit y!!!
c lng bng thng ca tn hiu iu ch:
Xt tn hiu iu ch dng: cy (t)=Acos[ t+k(t)]
pk=kPM:
(t)=m(t)
f
t
k=kPM:
(t)= m()d
Xt trng hp c bit k
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Signals & Systems FEEE, HCMUT
b) Bng thng ca tn hiu iu ch gc
c lng bng thng ca tn hiu iu ch:
Xt trng hp tng qut: tn s tn hiu iu ch thay i quanh
tn s sng mang c. Gi s l c- n c+ Bng thng
ca y (t) l 2 !!!?
Tm : i c
d(t) = +k
dtp p
d(t)=k' ;' max | |
dt
Nu chn k 0 th =0 y (t) c bng thng bng 0!!!?
Bng thng ca y (t) c dng: 2 +X MX=2
M2[ + ]Kt qu bng thng ca y (t) l:
f p M p
p p M p
FM: 2[k m + ]; m max | m(t) |
PM: 2[k m' + ]; m' max | m'(t) |
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Signals & Systems FEEE, HCMUT
b) Bng thng ca tn hiu iu ch gc
So snh vi AM:
Bng thng lun ln hn hoc bng AM
Bng thng c th iu chnh c bng cch thay i kp, kf
Li im: tnh chng nhiu tt
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Signals & Systems FEEE, HCMUT
c) Phng php iu ch/gii iu ch gc
iu ch di hp (k 0): c cy (t) Acos( t) kA(t)sin( t)
Tng t nh AM
iu ch di rng (tng qut):
c 1 c 1 c 1y(t)=Acos[ t+k (t)] Acos( t) k A(t)sin( t); k 0
2 2
c 1 c 1
A Ay (t)=Acos [ t+k (t)]= cos[2 t+2k (t)]
2 22
M c 1y (t) BBF:2, y (t)=Acos[2 t+2k (t)]
iu ch trc tip dng VCO
Gii iu ch: c c
dy (t)= A[ +k'(t)]sin[ t+k(t)]
dt
Tch sng ng bao
Gii iu ch dng PLL
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