Some Fourier transform pairs
Some Fourier transform pairs
Some Fourier transform pairs
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e −a|x| ↔<br />
2a<br />
a 2 + k 2<br />
e −ax cos bx U(x) ↔<br />
e −ax sin bx U(x) ↔<br />
(C.13)<br />
a + jk<br />
(a + jk) 2 + b 2 (C.14)<br />
b<br />
(a + jk) 2 + b 2 (C.15)<br />
cos k 0 x ↔ π[δ(k + k 0 ) + δ(k − k 0 )]<br />
(C.16)<br />
sin k 0 x ↔ jπ[δ(k + k 0 ) − δ(k − k 0 )]<br />
[ ( ) ( )] √<br />
1<br />
1 1<br />
2 be− 1 2 bx I 0<br />
2 bx + I 1<br />
2 bx jk + b<br />
U(x) ↔ − 1<br />
jk<br />
(C.17)<br />
(C.18)<br />
g(x) − ae −ax ∫ x<br />
−∞<br />
e au g(u) du ↔<br />
jk<br />
jk + a G(k)<br />
(C.19)
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