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Table with details about Fourier Transforms
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School of Mathematical SciencesENG2092
Fourier transform table
ENG2092 ADVANCED ENGINEERING MATHEMATICS B
Complex Fourier series expansion
A periodic function ( )f t with period can often be expressed in terms of the series 0T
0( ) nnin tf t c e ==
where 0 2 /T0 = and the complex coefficients are given by nc0 0
00
1 ( )nT in tc f t e
T= dt .
A table of some Fourier transforms
( )f t ( ) ( ) ( ) i tf f f t e = = F dt 1 1
1 ( ) ( )2
i tf f e d = F ( )f
2 ( ) (u t a u t a+ ) (2sin ) /a 3 ( )te u t for 0 > / ( )i i 4 ( )te u t for 0 > / ( )i i + 5 te for 0 > 2 22 / ( ) + 6 sgn( ) tt e for 0 > 2 22 / (i ) + 7 2 2/ ( )t + exp( ) 8 ( )t a i ae 9 '( )f t ( )i f
10 ( )i te f t ( )f 11 ( )t f t '( )i f 12 ( )f t a ( )i ae f
ENG2092 ADVANCED ENGINEERING MATHEMATICS BComplex Fourier series expansionA table of some Fourier transforms