Common Fourier Transform Pairsf(t), a > 0, > 0 F ()
eatu(t)1
a+ j
teatu(t)(
1
a+ j
)2p (t) =
{1, 2 t < 2 ,0, else
sinc(
2pi
)
(t) =
{1 2|t| , 2 t < 20, else
2sinc2
(4pi
)ea|t|
2a
a2 + 2
eat sin (0t)u(t)0
(a+ j)2 + 20
eat cos (0t)u(t)a+ j
(a+ j)2 + 20
eat2
pi
ae
2/4a
sinc
(t
2pi
)2pi
p ()
sinc2(t
4pi
)4pi
()
1
a2 + t2pi
aea||
(t) 1
1 2pi()
u(t) pi() +1
j
ej0t 2pi( 0)
cos (ot) pi [( + 0) + ( 0)]
sin (ot) jpi [( + 0) ( 0)]
sgn(t) =
{t|t| , t 6= 0,0, t = 0
2
j
cos(0t)u(t)pi
2[( 0) + ( + 0)] + j
20 2
sin(0t)u(t)pi
j2[( 0) ( + 0)] + 0
20 2
