[TS101] Traitement_du_signal_continu - Cours - 0

8/6/2019 [TS101] Traitement_du_signal_continu - Cours - 0

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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(,%


27/59



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,%


28/59



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


30/59



'(@,!'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%


31/59



= -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


32/59



!,&'!'&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@= /


33/59



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@=

<

,6'+

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

=UT

UT5

4UT

UT

=UT

KC

C D

QC D

,?6@+

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


34/59



'&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@=

'

&'

ICJD =

#@J@

@= /

@J@

@=

'

.GD(!'!") & 3 3 !&& 3 CFD D CM*D !( &!) _F_ _4!CM.l*#5D_ 3 ! )

&)(33&5k%,),()3)!'&'9(E!3)*','3&*FCFD3)A9('3,(,!(3',&*&!)>,&&!&!,()),),()3A(&*'35'(%49(")=>@,>&2)=>,(&)=>)@CD&=&&>&'$#3)=>33'#&(2&,'>()!),'2=,'&&>9('(43**,&O3**,9('O,(,*'()>!()&*(,'>!()&&!'&>*9(,=,,&,&>&!&!'&>9('3,'@')('O,'@')('&(%


35/59



A 6'

&6+

A'!'_*)$_&)A'!')!)(&&'(@)&(9(3(&$)%*),'@(&$)3A4UT(&$)3&'=UT3')&!,&)3!2)E,)(34UT%&,'!'&&&!,)&&'(&'(&(!!&>&&L3,)&`,&&)A'!'3*)$&('!')%*)3&,!(L"

^6C5D'('C5D>

^E6C5D'(6CD>^E'&A)!'&&3)'2(3,))()&3,&&&%$)>(*),(&*&E!'&!()&'))*>&&4,!'))!(LE!'&!()&'))*%*)3&,',(&*&'(M'(&E!'&!()&'))*%

!&6+

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,(,%


36/59



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%

$

!& 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.


37/59



3(4@$&3!&'3*)&*'&3A'33&&$(4*)&%**>)!&3!'!$'3$'(!&3*!

=

.

? I > ( )[ ]

!& 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&&'(@())%

!6+

GD9('3,(,"*)3&,,(&*&,,&!)*9(&'9('3,(,*!!Y3(4&'&3&,&>($'(!3&,))'&3)A4UT>)3(43&,))'&3&@)(&!&&&3)&'=UT%))!(&A,"

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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38/59



&

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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( )

= /

B

+ J 6 J( )

=

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I J( )= 6 J( )/ J( ) =#J

= /

J

=

K

)), !'&&3 3& !m)& 3& F'&% & ,'3'& 3 &2) !(@ L ',& ,'&3)!'&'3&!m)&@&E@&3(,,)3='(",(4,3'@LE)4

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*`)&)'&3A@&&2)%


39/59



,' ( *'&> ) !'& *9(, &A'2 && 3**,() !)\ ) @2) F !

4!CM.l*D&'" I > ( )=6 J( )/ J( )

=

#

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40/59



B ?'+

C9*""+

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')84!)38(*)3')&,2)',&3',,'%'9('3,(,&"

=UTO4UTP.4UTP=UT 3&,!' !)(& !,& 3 &' *',' & $) !'!'&` )) !,&)8,Y3&'!'&)&>&E )2&3)8!3 !'$')$$,%

4UT

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x >

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x >

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4UT =UT


41/59



4UT

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P

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( !' 3 @( 3 ) ',( 3& &()& 3&> ) ' I!'J ( !4!))*,()3&',W3&'&2&!)(&)'$&9()'&33% &, 2)', ()& !'( , !&' ,'&!'3 E , 9( '(& @'& !!) I*'3,J9(>'(&)&@'&>8&!&,'9(%,'''(@)I*'3,.J3(L*)>&9()&'!'& )&,'&!'3&9(>') 9(>&','23(%

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x >

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)(&!,&>)2)(,3&&'(&&()&,,&9(&3,,(3&&')('&%

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42/59



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