eec4-4a-ss-lecture-08.pdf

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



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 ()



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 ()



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)



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)



B lc thng thp l tng:

c

2

H()=rect( ) cc

h(t)= sinc( t)



B lc thng cao l tng:

c

2

H()=1 rect( ) cc

h(t)=(t) sinc( 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



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)



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)



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)


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)


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


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



S h thng iu ch:

AM cy (t)=m(t)cos t Tn hiu iu ch:



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)



H thng gii iu ch:

Yu cu: ng b sng mang my pht v my thu T/sng ng b


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:



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.


Tch sng khng ng b:

1

c>> M: lun tha trn thc t (500KHz-2MHz)



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)




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)



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


Phng php iu ch 1: iu ch AM-DSB + Filter

H()



Phng php iu ch 2: 900 phase-shift network



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



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


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:



V d v tn hiu iu ch PM & FM




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



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) |



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


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

eec4-4a-ss-lecture-08.pdf

Documents