Discrete-Time Fourier Transform
Xω=∑n=-∞∞xnⅇ-ⅈωn
X
ω
n
x
n
ω
n
(1)
Inverse Discrete-Time Fourier Transform
xn=12π∫02πXωⅇⅈωndω
x
n
1
2
ω
0
2
X
ω
ω
n
(2)
Relevant Spaces
The
Discrete-Time Fourier
Transform maps infinite-length,
discrete-time signals in
l
2
l
2
to finite-length (or
2π
2
-periodic), continuous-frequency
signals in
L
2
L
2
.
"My introduction to signal processing course at Rice University."