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7/13/2019 Tn hiu h thng-Lecture 06
1/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
Lecture-6
"0"00! T#n $i%u ' $% t$(ng
Biu din tn hiu bng chui FourierBiu din tn hiu bng chui Fourier
)i*u +in t#n $i%u -.ng t t#n $i%u tr1 gia3)i*u +in t#n $i%u -.ng t t#n $i%u tr1 gia3
C$u4i F3urier l56ng gi7C$u4i F3urier l56ng gi7C$u4i F3urier $'m m8 $C$u4i F3urier $'m m8 $7 ng ;a $% t$(ng i t#n $i%u tu?n $3'n7 ng ;a $% t$(ng i t#n $i%u tu?n $3'n
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7/13/2019 Tn hiu h thng-Lecture 06
2/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
)i*u +in t#n $i%u -.ng t t#n $i%u tr1 gia3
Biu din tn hiu da vo khng gian tn hiu trc giao:
Tm cntha iu kin nng lng sai s min:
Sai s:1
( ) ( ) ( )N
n n
n
e t f t c x t =
=
2
1
1 ( ) ( )t
n nt
n
c f t x t dt E
= Nng lng ca thnh phn sai s min: 2
1
N
e f n n
n
E E c E=
=
Nng lng ca thnh phn sai s
0 nu N
t!p c"s#
1 1 2 2
1( ) ( ) ( ) ... ( ) ( )
N
N N n n
nf t c x t c x t c x t c x t
=+ + + = $
%hi N & ta c': lu ( )*u +,- .ng / mt nng lng
1 2
1
( ) ( );n nn
f t c x t t t t
=
= 1hu2i34u5i65
2
1
*1 ( ) ( )t
n nt
n
c f t x t dt E
= Th7c: 8h9c:
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7/13/2019 Tn hiu h thng-Lecture 06
3/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier l56ng gi7
Khng gian tn hiu lng gic trc giao:
0 0 0 0 0 0{1, cos( ), cos(2 ),..., cos( ),....; sin( ), sin(2 ),..., sin( ),...}t t n t t t n t
0n : gi l hi th9 n 00
2,
T
=
Biu din f(t) trong khng gian tn hiu lng gic trcgiao:
0 0 0 1 1 0
1 1
( ) cos( ) sin( );n nn n
f t a a n t b n t t t t T
= =
= + + + 1 0
1 0
1
1 01
1
0
02
00
( )cos( ) 2( )cos( )
cos ( )
t T
t Tt
n t T t
t
f t n t dt
a f t n t dt Tn t dt
+
+
+= = 1 0
10
0
2; ( )sin( )
t T
nt
b f t n t dt T
+
= 1 0
10
0
1( )
t T
ta f t dt
T
+=
;it # )
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7/13/2019 Tn hiu h thng-Lecture 06
4/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier l56ng gi7
Biu din f(t) trong khng gian tn hiu lng gic trcgiao:
0 0 0 1 1 0
1 1
( ) cos( ) sin( );n nn n
f t a a n t b n t t t t T
= =
= + + + ;it # )
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7/13/2019 Tn hiu h thng-Lecture 06
5/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier l56ng gi7
Biu din f(t) trong khng gian tn hiu lng gic trcgiao:;> )?: khai t5i@n ABtC,6
DtEF
t54ng kh4Gng 0t0 0
2 / 2T = =
/ 2
00
10,504ta e dt
= =
/ 220
2 2cos(2 ) 0,504
1 16tna e nt dt
n
= =
+ / 2
20
2 8sin(2 ) 0,504
1 16
t
n
nb e nt dt
n
= = +
( )21
2( ) 0.504 1 cos2 4 .s in2nt ; 01 16n
f t nt n tn
=
= + + +
0 0 0,504C a= =
2
20,504
1 16nC
n
= +
1tan 4n n =
1
21
2( ) 0.504 1 cos(2 tan 4 ) ; 0
1 16nf t nt n t
n
=
= +
+
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7/13/2019 Tn hiu h thng-Lecture 06
6/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier l56ng gi7
nh tu!n hon c"a chu#i $ouri%r lng gic:
1hu2i 34u5i65 ch4 ABtC chH .ng t54ng kh4Gng tIttIJT0Ng4i kh4Gng tIttIJT0K
0 0
1
( ) cos( );n nn
t C C n t for all t
=
= + +0( ) ( );t T t for all t = BtC Li@u )iMn ch4 tin hiu tunh4n
;!= nu BtC$ tIttIJT0Li@u )iMn ch4 ABtC$ tIttIJT0BtC Li@u)iMn ch4 t>n hiu tun h4n )4 l!p l )?:
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7/13/2019 Tn hiu h thng-Lecture 06
7/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier l56ng gi7
&hu#i $ouri%r lng gic c"a tn hiu tu!n hon:
0 0 0
1 1
( ) cos( ) sin( )n nn n
f t a a n t b n t
= =
= + +
0 0
1
( ) cos( )n nn
f t C C n t
=
= + +
00
0
2( )cos( )n
Ta f t n t dt
T
=
00
0
2( )sin( )n
Tb f t n t dt
T=
00
0
1( )
Ta f t dt
T=
0 0C a=
n n nC a b= +
1tan nnn
b
a
=
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7/13/2019 Tn hiu h thng-Lecture 06
8/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier l56ng gi7
' d :
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7/13/2019 Tn hiu h thng-Lecture 06
9/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier l56ng gi7
' d *:
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7/13/2019 Tn hiu h thng-Lecture 06
10/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier l56ng gi7
+i,u kin t-n t.i chu#i $ouri%r:
0( )
Tf t dt<
TQn t
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7/13/2019 Tn hiu h thng-Lecture 06
11/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier $'m m8 $
/0 tn hiu h1 12 trc giao:
{ }0 ; 0, 1, 2,....jn te n =
&hu#i $ouri%r h1 12:
0
( ) jn t
nn
f t D e
==( )0
0
*1( )
jn t
nT
n
D f t e dtE
=
00
0
1( )
jn t
nT
D f t e dtT
=
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7/13/2019 Tn hiu h thng-Lecture 06
12/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier $'m m8 $
34i li5n h gi6a chu#i $ouri%r h1 12 0h7c 8 chu#i$ouri%r
lng gic:0cos( )n nC n t + ( )0 0( ) ( )
2n nj n t j n tnC e e
+ += +
nD nD
0 01
( ) cos( )n nn
f t C C n t
== + +( )0 00
1
( ) jn t jn t
n n
n
f t D D e D e
=
= + + 0jn tnn
D e
=
=
9.ng h1 12 8lng gic l
tng ;ngth
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7/13/2019 Tn hiu h thng-Lecture 06
13/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier $'m m8 $
0 0
2
2
n
n
jnn
jnn
D C
CD e
CD e
=
=
=
1,2,3,...n=
>h? $ouri%r:
0 0;D C=
1
2n n n
D D C= =8h\ Li[n ]: Bch@nC
8h\ pha: BlAC; ;n n n nD D = =
34i li5n h gi6a chu#i $ouri%r h1 12 0h7c 8 chu#i$ouri%r
lng gic:
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7/13/2019 Tn hiu h thng-Lecture 06
14/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
C$u4i F3urier $'m m8 $
+nh lC >arD%val :
0 0
1
( ) cos( )n nn
f t C C n t
== + +
2 2
0
1
12
f n
n
P C C
=
= +
0( ) jn t
n
n
f t D e
=
= 2 2201
2f n nn n
P D D D
= =
= = +
1Wng su*t ca t>n hiu tun h4n LXng t\ng cWng su*t ca t*tcG c^c hi
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7/13/2019 Tn hiu h thng-Lecture 06
15/16
Signal & Systems- Tran Quang Viet FEEE, HCMUT Semester: 02/09!0
7 ng ;a $% t$(ng i t#n $i%u tu?n $3'n
00
0
2( ) ;
jn t
n
nf t D e T
== =
( )j t j te H j e
input
_utput
0 0
0( )jn t jn t
n n
n n
D e D H jn e
= =
`nput ABtC _utput=BtC
(EF)
u!n honc=ng chukG vHi f(t)
+0 7ng c"a h th4ng EF& vHi tn hiu tu!n hon :
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7/13/2019 Tn hiu h thng-Lecture 06
16/16
Signal & Systems - Tran Quang Viet FEEE HCMUT Semester: 02/09!0
7 ng ;a $% t$(ng i t#n $i%u tu?n $3'n
' d :
2
2
2
( ) (1 4 )
j nt
nf t en
== (3 1) ( ) ( )D y t f t+ =( ) 1/(3 1)
( ) 1/(3 1)
H s s
H j j
= += +
2
2
2( )
(1 4 )( 6 1)
j nt
n
y t en j n
=
= +
2
r 2 2 2 21 1
8 1P 2 | |
(1 4 ) (36 1)ipple n
n n
Dn n
= =
= = +
rP 0.025
ipple= rP 0.05ipple =
