Discretetime Fourier series
x
[
n
] =
X
k
=
h
N
i
a
k
e
jk
(2
π/N
)
n
(1)
a
k
=
1
N
X
n
=
h
N
i
x
[
n
]
e

jk
(2
π/N
)
n
(2)
Continuoustime Fourier series
x
(
t
) =
∞
X
k
=
∞
a
k
e
jk
(2
π/T
)
t
(3)
a
k
=
1
T
Z
T
x
(
t
)
e

jk
(2
π/T
)
t
dt
(4)
Continuoustime Fourier transform
x
(
t
) =
1
2
π
Z
∞
∞
X
(
jω
)
e
jωt
dω
(5)
X
(
jω
) =
Z
∞
∞
x
(
t
)
e

jωt
dt
(6)
Discretetime Fourier transform
x
[
n
] =
1
2
π
Z
2
π
X
(
jω
)
e
jωn
dω
(7)
X
(
e
jω
) =
∞
X
n
=
∞
x
[
n
]
e

jωn
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This note was uploaded on 02/12/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Spring '06 term at Purdue.
 Spring '06
 V."Ragu"Balakrishnan

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