Tabela de transformadas - Completa

Prévia do material em texto

TRANSFORMADA DE FOURIER – FUNÇÕES CLÁSSICAS 
 
)(tx )( fX Obs: 
)(tret )(sinc t 
 
)(ttri )(sinc2 t 
 
)(tue ta− ifa pi2
1
+
 0>a
 
)(tue tz− ifz pi2
1
+
 0)Re( >z
 
|| ta
e
−
 
222 4
2
fa
a
pi+
 0>a
 
)sgn(|| te ta−
 
222 4
4
fa
if
pi
pi
+
−
 0>a
 
)(tute at− 
2)2(
1
ifa pi+ 0>a
 
|||| taet − 
2222
222
)4(
42 fa
fa
pi
pi
+
−
 0>a
 
|| tate− 2222 )4(
8
fa
iaf
pi
pi
+
−
 0>a
 
2ate−
 
22 f
a
a
e
pi
pi −
 
0>a
 
2atte−
 
222/3 f
af
a
i e
pi
pi −






− 
0>a
 
TRANSFORMADA DE FOURIER – FUNÇÕES GENERALIZADAS 
 
)(tδ 1 
)sgn(t 
ifpi
1
 
 
)(tu ( )f
if δpi 2
1
2
1
+ 
 
iate ( )piδ 2af − Ra ∈ 
)cos(at ( ) ( )pipi δδ 221221 aa ff ++− Ra ∈
 
)(sen at ( ) ( )pipi δδ 221221 aa ff ii +−− Ra ∈
 
)sgn(teiat fa
i
pi2
2
−
 Ra ∈ 
)(tueiat ( ) fa
if a
pi
δ pi 22
1
2
−
+− Ra ∈ 
||tia
e 2222
22
4
2
4 fa
aif a
pi
δ
pi −
+





− Ra ∈ 
2iate− ai
f
e
ai
22pi
pi
−
 
0≠a
 
t ( )fi δ
pi
′
2
 
 
nt ( )fi n
n
)(
2
δ
pi






 
 
|| t 222
1
fpi− 
 
 
 
TRANSFORMADAS DE FUNÇÕES RACIONAIS 
 
t
1
 
)sgn( fipi− 
 
2
1
t
 ||2 2 fpi− 
 
at +
1
 )sgn(2 fi iafe pipi− Ra ∈ 
ibt +
1
 )(2 2 fui bfe pipi −− 0>b 
ibt −
1
 
 )(2 2 fui bfe −pipi 0>b 
zt +
1
 )(2 2 fui izfe pipi− 0)Im( >z 
zt +
1
 
 )(2 2 fui izfe −pipi
 
0)Im( <z 
22
1
at +
 
||2 fa
e
a
pipi −
 0>a 
22
1
at −
 
( )||2sen fa
a
pi
pi
−
 0>a 
TRANSFORMADAS DE SINAIS MODULADOS 
)cos()( attx ( ) ( )pipi 221221 aa fXfX ++− Ra ∈
 
)(sen)( attx ( ) ( )pipi 221221 aa fXfX ii +−− Ra ∈
 
)cos()sgn( att 222 4
4
fa
if
pi
pi
−
 Ra ∈
 
)(sen)sgn( att 222 4
2
fa
a
pi−
 Ra ∈
 
)()cos( tutbe at− 22)2(
2
bifa
ifa
++
+
pi
pi
 Rba ∈> ,0
 
)()(sen tutbe at− 22)2( bifa
b
++ pi
 Rba ∈> ,0
 
t
at)(cos
 
( ) ( )[ ]afuafu
a
i
−−−− pipi
pi 22
 
0 , ≠∈ aRa
 
t
at)(sen
 )/( afret pipi ⋅
 
0 , ≠∈ aRa
 
MISCELÂNEA DE TRANSFORMADAS DE FOURIER 
 
)(sinc2 tt
 
)()sgn(
2
1
trett
ipi 
)()sgn( trett )(sinc2 2 ffipi− 
)arctan(t
 if
e
f
2
||2pi−
 
 
t
e
t ||−
 
)2arctan(4 fi pipi−
 
 
)2cos( θpi +tfc [ ])()(21 cici ffeffe ++− − δδ θθ RRfc ∈∈ θ , 
)(trete Tiat ( )[ ]pi2sinc afTT − Ra ∈
 
)(|| trete Tta− 
( )
)4(
)cos(2sen4
4
2
222222 2/ fae
TfaTff
fa
a
aT pi
pipipi
pi +
−
+
+
 0 ,0 >> Ta
 
22 atet −
 
22
2
2
2/5
2
f
afa
a
e
pi
pi
pi −






−





 
0>a