[ts101] traitement_du_signal_continu - cours - 0
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D
*5#.5#.
& ) 2)(> ' '(@ )& !'!& &&))& 3 ) 5> !,() ) !'! 3)% !'3( 3 ,'@')(' 3 &$(4 3&,& !!Y 3& ) 2)(% ) & 3* !)A9('"
UT.UT = UT%.U T=
+
5@&9(E))&A,"
UT =(.
/CD >(
(
+
(
.GD&*'35'(3&,C5D"5!(3&,!'4,C,A&E3!)A33A(*',','(D3&)A&!,3&*9(,&3(&!,3A(&$)3&,9(),'9(>,A&E3E3(*'!'39(%>&)A'&(!!'&9(,,),()3@LD!&)D!(,),()(
(9(>)&,&&" 3 ,'&3 9(A( '2 * 3A,))'& 3 4UT> 3A(& & 3 '9(!'))4UT()&(*L3A'2&@'33(*>
3 ,),() 9(A('2*3@)(&3/> 3A(& & 3A,))' )&!,%
'(&))'&4)&,'&9(,&3,&3(4,'&%D '3('23A,))'&34UT"
'&3'&(*L3A'2&@'!'))cUT>3)$(/O"cUTO!'(/gg/PCD>cUT&())!'())(&
*L&3_,$()_% 3! )'& && 3**,() 9( )A4!&&' 3 ) 5> '2 )A4!&&' 3 )5_E!'&_>!'&!'())$)A,(/O/"
/CD = UT >(
= /
B
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)'3('23A,))'&,'&3&!'(),),())'(*'&)&!,,),()") !'3( 4UT%cUT & 3(& 3& )A&!, 3& *9(,& ! ) !'3( 3 ,'@')('
/SC% )A) ( 3 ) ,'@')(' & )A!()&' 3 ,> , () `)((&>)*L,$()>(,((*LA'!'(&*'35'(
(). ))(&> ) &$*,' !=&9( 3( &!, 3A( &$) ' !'39( E 3( *>,),()&((@))!')*>A&!&'!)(&&&&'()@3&9(&'&%9(!(L'(*'&(,>,A&9(!)(&&$3>'&&@&)A)'%
2D '3('23@)(&,),()&",),()((9(C,A&E3(,E &*&D!(!3*'*'(9(A(
'2*3@)(&!'(/)>,9(,'&!'3E(,))'$3(&!,%')!&3A,))'$>)5E!'&3@CW()*D"
/U@T = UT >C@D(
= /
B
9('&9()*',''2(>KUWT>&(*','3&,%C,)&),&
!9(D &(*,'3)A@))*'3)>UC.#D# ] 1!'&3@'L,),()&%&3(&!,&33(&!&)'%
9(&'3("9())@)(3'E N@)(*2)3'($3*&&3!&' & ,&& 3 '2(4 ,),()&> !(L 3'3&% @)( )@> (,'> 3' ( &() !3 & !(L @, ! 3A*'' (> )&*'' @& !!)9( ( &!, ,))' ! !& 3A'2 ) &$)'$)%((&>)'3'>3ME,'!'()A,))'$!')>!'&&3(9(@)!'()A,))'$*9()%DE!(,FE4!!!5'G$'!E!4!!3H(,IJ-'(&33(&'&9()&(')!)(&,''9(,),(),'&!'3E"
=.
(/=
.
B( 9( 3*@> &!' 3& )A9(' 3 ) 5 E !'&> 3' )A4!&&' 3 )&*'35'(3&,C5D"
/U@T = UT >
@.
B
=/
B
*','3&,> !'39(> 3 !'3 C' 3 9( ,))'& !& 3' ,))'&
*9(,D%5@&9(E))!'(4!&&'"
UT =
B/U@T
>@.
B
@= /
B
&3(4*'()&&'&!',&>()$',),())A(!'(>&&$'&&&3**,()&>,),())A(%9((&&>,)'(&&()(!(!)(&)'>9()5@&&))(&&!'39(>3!'3%2)(,,'&()&3**&!&3(,),()>3&)A&!,3(!&3)*9(,>,, &(!!'& ! 3A( &$) )'$9( *,@ &() ) !& *9(,%
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GD&*'35'(!3"D '23A'!'&,&&&!'(),),()3)5"
(!!'&'&4UT)`!'(,),())!))3A(3&@)(&3A(5
^()!),'&3(=!4UT%M.W#^CD33'&3&&()&3&()!),'&!,3&&',&&&%'(')>!'(!'&3(&!,>&ee>
.,=,)&C,=,)O33'
()!),'D%,**&E()!)!3(4!(&9(A)*((&&,),())!$%
& , &'> ' &(!!'& 9( )& @)(& 3 M.W# !(@ L ,),()& ( *'& !'(
'(&>$&'"))&3!3!&3&@)(&3&,))'&% !!),'(9("(!!'&'& ) ,),() !& ) 3A( 5 E /.0 O .
/ !'&> ()& ( ,,( C@'
,!_=&3&*)&(9(&_D!'&&3(@&&3,),()31/&!,=,)>E!3A(&$))'$9(4CD,))'!)*','3&,4UT%!&,),()&)'&,O.4C./D.O//&%&)!'&&2)3A2)(),!&,),())&,,&9(&!'))&34UT>))))$(3)*L3',(N&,,3&&'(&&()&'&,&!'&&2)&"
D ),),()3)5,&&'&3!&9()A,9(&'!)3&,))'&
34UT% 3( !&!'(*(,'&>& &),),()3)5&&&()j,>)&&(3&'>3','!,%
2D )A,9(&'3&,))'&34UT,&&'&3!&9(),),()3A(&!,!)5% 3(4 && 3A,9(&'&) 4& (!&'!3)9() )A= !&3A,9(&'3A,))'&")=3',!3A*''%
,D ,9(&',),()')L3(>,A&),&'!)9('(&,'&3'&,%)'&/OO,%
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4CD
K
;
,'(&&'(&)'3A)$'3A),!')%'(&))'&3',)!,!%&(!!'&9()'23A,))'&&(!(&&,33(4>&'"
O.
>()%
4UT!'&&3)'&())('2!3A,))'&>)5!(&A,"
/U@T = U.T >
0 @
B
= /
B
.
+ U. + T >
0 @
B
= /
B
.
>
.@
B
$'(! )& ,))'& !& 4U.T )& ,))'& !& 4U.PT 3(4 &'&3&,&%,(3,&3(4&'&&(5E#.!'&>3!'33A,))'$. %9(5&2&Z!'39(>3!'3#.!3',),),()3#.!'&3(&!,E!'&%'23,=,)&,&&&!'()A&2)3(,),()&
.C3(45D4.C#.D.O
.>
&' ( '2 3 ,=,)& 3(4 *'& !)(& ! C' $)$ )& 3(4 '!'& &(!!)&!!(&")A33'3&3(45>)()!),'3)3(4!)A4!'))
D%
,,( 3& 5 E #. !'& ,'!' E &' '( ( '2 ! 3A,))'& !( L$)3,'!'&%!',3&M(&9(AE'23&5E3(4!'&[3'9()'23,=,)&)'&,&&&&%%)$'&!!)_&*'35'(!3_C5&5'(&*'"55D%
'2(&&@&4&!'()&B(@!9(>&)!,!&,)(9(@3AL !&% ''& 9( 2 9( , )$' &' *9( !)'= ! )& &=&&(9(& 3A)=& &!,)> 3A(& !',3&> !)(& !*'& E ,& !'& 3 @(> &'$)!)'=&C''(@(4!)4,,D%
!!),'(9("@*&&3**,()9(3&'4!)>''2@,)A),!')* 4OF%0GD'(&()9(&'3&*L&"(4,&!9(&!(@&!&!'()A!!),'3)5E(&$)"^4UT&E3(*>3',E&!,E&(!!'*"),),()3)5&!,'!)')3&,))'&'()&>*'(3&,))'&3A(&!,2'C!)*)
!)D>9(&3',(!!'4'3(&!,)%^4UT&E3(*",A&),&9(A)*(@&$ !',)A)=&&!,)@'((,9(3A@&$'%A!!'4'3) ) )(*9( 4UT@ L'9(!'))%**)A!!),'3)5@&(&!,,),()@3'(&$)4AUT!'39(C3!'3 /D [ 4AUT @!& 3& 3&,'(& (4 !'& 3,,'3 )& 3**&!'3&% & 3&,'(& ,'&!'3' E 3& ,'!'&& (& *9(,& 3& ) &!,&(!!'&L,)(34UT>9(&*,)(3(&$)!'39(4AUTb4UTC'&),&&!,()'V4UT&M(&!'39(3!'3/D%
(>,9(__C,A&E3,))'D34UWT,'&!'3*E(_'9(_34AUT%
()!),'!
M.W#&)(3!&$4U.T4C.PT
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'(@,!'2)>3A(&*L&9()*L,$()&'()&&` )('2M,*&3A'3( ( ,'( !')) (4 !'& 3 ,,'3 3& 3**& !'3&> ( )A!)(3 3& !& 3& ,))'& 3 4UT% & )A&!, 3& *9(,&>
,' 3ME 3> ) *L 3@ &A!!', ) !)(& !'&&2) 3 )A!()&' ( 3&, []>)(3),'@')('% '2(&& *L& 4& C$() '( 3 :)> :),W> $> $>
X&]D'(& '** ( ,'!'& 3** ) ')$&& 3&& '9(!&&)'!!'3&&(!!)&%,!'3@(>)*L,$()&)))(!'(3&$(3(4&3M,&>&)!!'(3,3&&3*2)!)(3%1GD$(4E!)(&(&3&'&"A)=& 3 5'( !( &A!!)9( E 3& &$(4 E !)(&(& 3&'&> 3' ,& &'&!)&'!)(&!'))&%A&)'&*'3),$%)=&3A$&*4&"3(43&'&&!)&%)=&3A$&&"3(43&'&&!)&(3&'!'))%49("
(UTO(&!*(,'> UTO(!()&*(,'>
5'(&*'>3&,5'(&*'>*&5'(&*'C55D>c3'c$>'3)&"c@)>c@))=&&>3&3&,"&c''&>*'38'3"c@*'>&()"&')3>I&$'F','**,&3''4,3,&')3J%
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= -3/
6+
'(& '(& &&'& , E ( &=& &(&,!2) 3 *' ( &$) 3&, 4UT C9(,'&()AD((&$)3&,=UTC9(,'&()&'D%&=&E!&3&,!(L,,&!)&!'!&&(@&"
"&4UT3'=UT&4.UT3'=.UT)'&4UTP24.UT3'=UTP2=.UT&)&=&&)>23&,'&&>
4/"&4UT3'=UT)'&4U/T3'=U/T9()9(&'/>
""&'(&$)4UT3A!)(3*3'(&$)=UT3A!)(3*>
"&,(&)(&=&)9(A(&$)3&'=U /T&3!334UT!'('( /dC)A**!(!&!,3),(&D%'()A&&)>(&=&3&,)&,,&>(,'4>!&'9('(43**,&C9(@) E )A9(' 3**)) 3& &=&& )& ,'(&D> ! && !'&&!()&'))&UT '9(&CM*D>!&*','3&*FCFDC@'!)(&)')3*'3,&&D%9(!!',!),),()3)!'&3(&=&E(
9(),'9( C)=&D> & )A()&' 3 !)(&(& !!',& & $) ,&& !'(,',@'(&=&E!3A(,3&,$&C&=&D%
'6689+
GD'3(,'"&&=&&3&,&)&&')&2)&!&&2)$3'&'!'&32&")A33'>) ()!),' ! ( ,'& ) & '% & '!'& *$( 3& )& 2)',&*',')& )& ()&& 3& )& &,& 2)',& !& ( &=&% 3&&'(& !&(,'&>&=2')&)!'33A,))'$%
4UT =UT
9('(43**,&UTCM*DCFD
4UT
=UTO4UTP4.UT
4UT
4UT
4.UT
>
=UTO4UT
=UTO4UT
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!,&'!'&32&>'!(&=&'(&=&3&,)%!)(&>''&9()A9('3,(,&)_'(_3(&=&"))!&)&'!'&)&,,'!)&!9(3&)&=&!=&9(%.GD&,!'3A(&=&!&'9('(43**,&")A&>)&&=&&3&,&)&3)@E)(&'3&,))'&=UT9(&'3&,'2&'&)&3&&!&&!&&&C$)*((&!'()&&=&&',(&(4D@())3&@)(&!&&&3&,))'&3&'%'((&=&,(&)'3&),&$)"
9 [ ]= #@ @[ ]@= /
+ @9 @[ ]
@=
'
&=&&6&A)4&('&(@)('())!'()&,'&& W%,'3'
)!'(=UT&E!,&3&,,&%'(M'(&3&,,&>)&=&&34'&9&)A3,)!)(&)@3&,'&&'())&W%')3ME3>)A9('3,(,&)_'(_3(&=&%)((&>))! !& 3A2) ( 4!&&' )=9( 3 ) *',' 3 &' 3& ) ,& 'V ( ))4!&&'&3&!'2)!'()A%))(&))3'$)!&3A*''9(E)!'&*9())C'9(D3(&=&%
/3+
'&'& UT ,' ) !'& C3 !()&'))D 3A( &=& 3&, ) ,(&)
@E)A!()&'(3&, UT%'(&))'&3&(!!&3'C,9(@3@,)A9('3,(,D9()!'&!()&'))3,,'!))&=&"3A(&&9(A))!3,),())!'&E(&$)9(),'9(UT%
5
5
S
4UT
=UT
UT5
4UT
UT
=UT
KC D
C
D
QCD
UT&,(&)>'!(,9(
UTOU/T% UTPUT% UTPU.T% U.TP])&=&&)@>!3*'>&!'&!(L)'&**,@,),()H))&)'&3)*'
=UTOU/T%UTPUT%UTPU.T%U.TP]&'&'(&*','3&
9UT = U@T%4U @T@= /
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9(' & 4' / 3( &=&% )) ! 3 ,),() ) !'& 3A(&=& E ( 9(),'9(> ,'&& & !'& !()&'))% ) &=& ',(&))&2'&3&''3)A9('3,'@')('3PE)A*%))(&>),'3'3&2)3A(&=&!(,L*'()"(&=&3&,&&2)&&!'&!()&'))&&'2)>&'
4U@T@=
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3*'>)&*'35'(3&,C5D3UT,'&()!'&*9(,CM*D3A(&=&3&,%9(,'!)4!(L$!9(3'(2)!&>
!&''3()&'$(>'(&3(4*','3)*9(,*'(3)!()&'%&=&),'@(&$)3A&(&'f3)(&$)3L*9(,>&3'
)A!)(3)!&3!33%,'@')('!'))()&!)(&(!'(),),()3)&'3A(&=&>!(,L!),!(&!)!'3(3&)A&!,3&*9(,&%
5
5
S
4UT
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UT5
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GD*'4!)&" L 9( !'( )& &=&& )& ,'(& ) 4& 3& @$& E ()& ) @2) !'3(!)&*'3!),>'&'(@L!'()&&=&&3&,&)&E()&)@2)F'3(!)_&*'F_%&*'FCkDKCFD3A(&$)4UT&3*!"
/CJD = UT%J
=
&!'!&&&))&3)&*'F&'C)!9('3())3)&*''D"
UT + #.UT /CJD + #/. C D
UT
U T J
U T J
/CJDUT.UT /CJD%/. CJD
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'&9()&,'3'&)&&'())&>)&&(!'&&2)33*66
@CFD3A(&=&3&,3')A&4UT)&'=UT"
ICJD =6CJD
/CJD *' $) 3 CFD & *,) '2( E ! 3 )A9(' 3 ,(, 3' )
&*'3'
6CJD = #@J@/CJD
@= /
+ @J@6CJD@=
'
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ICJD =
#@J@
@= /
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'
.GD(!'!") & 3 3 !&& 3 CFD D CM*D !( &!) _F_ _4!CM.l*#5D_ 3 ! )
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A 6'
&6+
A'!'_*)$_&)A'!')!)(&&'(@)&(9(3(&$)%*),'@(&$)3A4UT(&$)3&'=UT3')&!,&)3!2)E,)(34UT%&,'!'&&&!,)&&'(&'(&(!!&>&&L3,)&`,&&)A'!'3*)$&('!')%*)3&,!(L"
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GD9('3,(,"& *)& 3&,& ',(&*& !'&&3 !& 3 2'(,) 3 ,',' ` )( 9(' 3,(,*3',!!Y(&()&'3&,>&'!'((*),(&)"
9 [ ] = # [ ] =/
&(,(=!9(>3&@&)C'V&())@)(4UT&'&D&3',,'%
3
'&
3
'
3
'
3
.GD!'&!()&'))"!!)'&9(A)&A$3)A4!&&'!,()UT3)&'=UT)'&9()A&)A!()&'
(3&,UT%)A9('3,(,>)!!Y3',9(4 [ ] = #/ [ ]+ # [ ]+ #. .[ ]+ %%% + #B B[ ]
= # [ ] =/
B
*)',(&*&3','(M'(&&2)!(&9(&!'&!()&'))&E3(*")&' @ E F' ( 2'( 3 P ,))'&% & ,'**,& ' ()& 3 UT &' )&
,'**,&3)A9('3,(,%
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GD!'&3,))"!!)'&9(A)&A$3)A4!&&'!,()3UT3)&'=UT)'&9()A&)A,)'(3&,(UT%'&'&W!'&*`'!()'&,9("
@[ ]= #/ + # + %%% + #@ !'(/gWd @[ ]= #/ + # + %%% + #B = B[ ] !'(gW
(@9(3UT&()'(!&>)*)_!&&_)$,'(,'&'(!&%0GD!'&'9("),()'&)&*'F3)A9('3,(,%)@"
6 J( ) = #J
/ J( ) = /
B
I J( ) =6 J( )
/ J( )= #J
=/
*','3&*CFD!&9(3&F'&>,9(,'*),,'(M'(&&2)3&*)&',(&*&%!'&*9(,&A'2&&3**,()!)\)@2)F!4!CM.l*D&'"
IC>D = #> .(
=/
!'&*9())&3',!'3()>!!&>!'39(3!'3$)E) *9(, 3A,))'$ 5% &!,*,' 3A( *) 3&, & 3', '(M'(& 3' &()A@))*'3)U/g*g5#.T%1GD5)&E!&)"&'3&*)&)&9()&,'**,&2 !&(&=%',&,'**,&&'(&& )& @)(& 3& ,))'& 3 ) !'& !()&'))> , ,,&9( !( L@&()&,',3&&'(&3&),&'V)&,'**,&&''(&!'&*&>&(@9(A)&&''2!CE$(,D'(!CE3'D%
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!& 3 CM*D @ )'& ) *',' 3 ) *9(, *% )) ,,&9(,'!'3(4@$&%!&3!(3(,'!3(4C,&!D'(!&9(3(4C,&!D3('23,'**,&'&&3A!&3()!),'C@'3&&D%
T TT T
T TT T
+ + +
+
2/ 2 2.
4UT
=UT
2.
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3(4@$&3!&'3*)&*'&3A'33&&$(4*)&%**>)!&3!'!$'3$'(!&3*!
=
.
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!& 3 !'!$' 3 $'(! & 3', ,'&> 9()) 9( &' ) *9(, 3& &$(4,'&3&"3(4&(&'f3&3*9(,&3**&&'3&339(!)(@& 3( *)% A& , ** 9( 4!)9( 9( )& *'& 3A'3 3& &$(4 &' !&3*'&!)!&&$3&(*)E!&)% '' 3 !& ) & &&)) *)$ (9( , ) !& 3 ) *',' 3&* A= & M& ,'&> &, 9(AE ,(& 3( !& ,&& E )A4,(' 3)A)$'%''&'&,)*)$)'$9(,>3&)&23&!&&&3&*)&)!&&$),'&>L&&'(@())%
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9 [ ] = # [ ] =/
B
+ 9 [ ] =
K
O/ C&() 4& ) 3(4 &' 3&,D ) *) & )'& 3 6% !9(>)A9('3,(,!(3,L&!'&&'(&)*'3(&,2)',,,'",A&)6%
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&
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'(*'&>&)*)&&2)> 4 [ ]
/ %&@)(&3&,'**,& 3)&2)%&
,'3'&3&2)!(@L',&E!3A(4!&&')=9(3UT%GD!'&'9("@, ) L 3, 9( !'( )& *)& ' ,(&*&> ) & !'&&2) 3A2) ) *',' 3
&*F"6 J( ) = #J / J( )
= /
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I J( )= 6 J( )/ J( ) =#J
= /
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=
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