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8/18/2019 Serie de Fourier v2
1/6
!"#$%&'( *
+,#-,.,/%"0$1/ 2, 3,4"',. #,-$12$0". ,/ .,-$,. 2, 5(&-$,-
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!"#$%& ( )( *+&*$"%(% %" ,-*"+*&,$.$/01 )( +",*-",2( %" -0 ,$,2"3( 456 ( .-()7-$"+ "02+(%( 7-"
.&0,$,2( "0 -0( .&3#$0(.$/0 )$0"() %" ,"8()", #9,$.(, ", )( 3$,3( .&3#$0(.$/0 )$0"() %" )(,
+",*-",2(, $0%$:$%-()", ( .(%( -0( %" %$.;(, ,"8()", #9,$.(,< =0 ",2" .(*$2-)& ," "0>&.( )( (2"0.$/0
"0 ,"8()", *"+$/%$.(, .&02$0-(, ? %$,.+"2(,<
=, $3*&+2(02" *(+( ") ",2-%$& %" ,$,2"3(, 456 ") +"*+","02(+ )(, ,"8()", .&3& .&3#$0(.$&0",
)$0"()", %" ,"8()", #9,$.(, 7-" *&,"(0 )(, ,$@-$"02", *+&*$"%(%",A
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,"8()",<
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8/18/2019 Serie de Fourier v2
2/6
L(+( ") %&3$0$& %$,.+"2&
# ())# * )
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+'
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8/18/2019 Serie de Fourier v2
3/6
"02&0.", ,$ + 6 )
$O
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# ! " "3+ && 0)-O " %" # *
+ #&'
'
3+ 4
3+ #B
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# !" "&& 0+ -O" %"
@#$/- $,.$,-,"#/()%",- &, 5/ + "!.&, + -O " & '&) + -O " "/
# !" "#3O+E*+ #B
'
9&3: .=+ .&, + -O " + 0 =+ '&) + -O " + 0 >+ .&,+ -O " &>+ '&) + -O " /
# !" "#3O+E*+ #B
'
(=+ .&,+ -O " &>+ '&)+ -O " )
Dado que es una función compleja y su conjugado:
Z = a+jb + a-jb = 2a
8/18/2019 Serie de Fourier v2
4/6
# !" "#3O+E*
+ #B
'
=+ .&, + -O " &E*+ #B
'
>+ '&) + -O "
>,-/$$%55% ./$/ ,"(%"#$/$ 5/- (%1.%","#,- D? 9 (? &, 5/ 2' +?@ "
# !" ".&, + -O
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," $02"@+( "0 -0 *"+$&%&
$O
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4
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=+ .&, !+ -O " ".&,!+ -O " "%" &$O
4
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!
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B
E.&,!+ ++ "+
B
E .&,!+ &+ "#
B
E !
B
E '&) !+ ++ "+
B
E '&) !+ &+ "#O
E*+ #B
'
=+ $O
4
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E
.&,!+ ++ "+B
E
.&,!+ &+ ")%" #=+ 4
$O
4
# ! " ".&, !+ -O" "%" #=+ 4
=+ #B
4 $4
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"0.&02+(+"3&, )( .&3*&0"02" .P
#! " "#3O+E*+ #B
'
=+ .&, + -O" &E*+ #B
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$O
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=+ .&, !+ -O " " '&) !+ -O " "%" &$O
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"3*)"(0%& $%"02$%(%", 2+$@&0&3Y2+$.(, *(+( )&, (+@-3"02&, %" )(, ,-3(2&+$(, %" #P ? .P
+",*".2$:(3"02"1 "02&0.",AB
E '&) (!+ ++ "- O" )+
B
E '&)(!+ &+ "-O " )#O ! &
B
E .&, (!+ ++ "-O " )+
B
E .&,(! + &+ "-O " )#
B
E
8/18/2019 Serie de Fourier v2
5/6
"02&0.",
$O
4
# ! " " '&)!+ -O " "%" #&*+ #B
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3O# B4 $4 # ! " "%" # B
4 $&=
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3 %" # 34 ( " ) =
&=
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# !" "&& 0+ -O " %" #B
4 $&=
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4 "
%" #3
4 ! &4 0+A3"(&& 0+A 3
4 " ) =&=
3+ # &3 0+A3
(&& 0+A3 =
4 && 0+A3
=
4 )# 3+ 3 ( BEC !&
0+A3 =
4 &&& 0+A3
=
4 ")
#U#
(
5
8/18/2019 Serie de Fourier v2
6/6
3+ # 3
+ 3,$0 +A 3
=
4
L(+( ") .(,& ( Q E :&)2,1 5 Q _ ,"@ ? %(%& 7-" 5 Q _# "02&0.", # Q B
(O Q B :&)2
3+ # E
+ 3,$0!+ 3E "
# !" "#33 *
+ #&'
'
( B+ ,$0 !+ 3E "& 0+ 3
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(+3/0$.( %" UE`ISa J< 4(, >-0.$&0", %" ,- *+$3"+ ? 2"+."+ (+3/0$.( ,&01 +",*".2$:(3"02"A
#B! " "#E3 &
0 3E
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#S!" "#&ES3
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