常用Fourier变换表

Signals&Systems-ReferenceTables1TableofFourierTransformPairsFunction,f(t)FourierTransform,F(
)DefinitionofInverseFourierTransform






deFtftj)(21)(DefinitionofFourierTransform



dtetfFtj

)()()(0ttf
0)(tjeF


tjetf0)(
)(0


F)(tf
)(1

F)(tF)(2

fnndttfd)()()(

Fjn)()(tfjtn
nndFd

)(

tdf

)()()0()(


FjF
)(t
1tje0
)(20


(t)sgn
j2Signals&Systems-ReferenceTables2tj1)sgn(
)(tu

j1)(



ntjnneF0




nnnF)(20

)(trect)2(
Sa)2(2BtSaB
)(Brect
)(ttri)2(2
Sa)2()2cos(trecttA22)2()cos(


A)cos(0t

)()(00





)sin(0t

)()(00




j)cos()(0ttu

22000)()(2








j)sin()(0ttu

220200)()(2









j)cos()(0tetut


220)()(


jjSignals&Systems-ReferenceTables3)sin()(0tetut


2200)(


j

te

222

)2/(22
te
2/222


etetu

)(
j
1ttetu

)(2)(1
j

TrigonometricFourierSeries




1000)sin()cos()(nnnntbntaatf

where





TnTTndtnttfTbdtnttfTadttfTa000000)sin()(2and,)cos()(2,)(1


ComplexExponentialFourierSeries




TntjnnntjndtetfTFeFtf00)(1where,)(

Signals&Systems-ReferenceTables4SomeUsefulMathematicalRelationships2)cos(jxjxeex

jeexjxjx2)sin(

)sin()sin()cos()cos()cos(yxyxyx

)sin()cos()cos()sin()sin(yxyxyx

)(sin)(cos)2cos(22xxx
)cos()sin(2)2sin(xxx
)2cos(1)(cos22xx
)2cos(1)(sin22xx
1)(sin)(cos22
xx)cos()cos()cos()cos(2yxyxyx)cos()cos()sin()sin(2yxyxyx

)sin()sin()cos()sin(2yxyxyx

Signals&Systems-ReferenceTables5UsefulIntegrals
dxx)cos()sin(x
dxx)sin()cos(x

dxxx)cos()sin()cos(xxx
dxxx)sin()cos()sin(xxx

dxxx)cos(2)sin()2()cos(22xxxx

dxxx)sin(2)cos()2()sin(22xxxx


dxex
aex

dxxex

21aaxex

dxexx
2

32222aaxaxex


xdx
x


ln1

222xdx
)(tan11

x