Fourier Transform Table ( )x t ( )X f ( )X ω ( )tδ 1 1 1 ( )fδ 2 ( )πδ ω

0( )t tδ − 02j fte π− 0j te ω− 02j f te π 0( )f fδ − 02 ( )πδ ω ω−

0cos(2 )f tπ 0 0

1 ( ) (2

f f f fδ δ− + + ) 0 0( ) (π δ ω ω δ ω ω− + + )

0sin(2 )f tπ 0 0

1 ( ) (2

f f f fjδ δ− − + ) 0 0( ) (jπ δ ω ω δ ω ω− − − + )

( )rect t sin ( )c f sin

2c ω

π

sin ( )c t ( )rect f 2

rect ωπ

( )tΛ 2sin ( )c f 2sin2

c ωπ

2sin ( )c t ( )fΛ 2ωπ

Λ

( ), 0te u tα α− > 12j fα π+

1jα ω+

( ), 0tte u tα α− > ( )2

1

2j fα π+

( )21

jα ω+

| |, 0te α α− > 2 22

( (2 )fα

α π+ 2 2

2( ( )

αα ω+

2te π− 2fe α−

2fe α− sgn( )t 1

j fπ 2

jω

( )u t 1 1( )2 2

fj f

δπ

+ 1( )j

πδ ωω

+

( )d tdtδ 2j fπ jω

0( )n

t nTδ∞

=−∞

−∑ 0 0

1

n

nfT T

δ∞

=−∞

−

∑

0 0

1 2

n

nT T

πδ ω∞

=−∞

−

∑