WOLFRAM|DEMONSTRATIONS PROJECT

Fourier Transform Pairs

​
f(x)
top hat
exp(-a
2
x
)
2
x
exp(-a
2
x
)
exp(-a x)
a
1.062
Here are four examples of Fourier transform pairs related by

f
(k)=
1
2π
∞
∫
-∞
f(x)
kx

dx
, where the slider
a
is a width parameter.