Digital Signal Processing Reference
In-Depth Information
Table 11.7. Fourier transforms for different types of waveforms
Time domain
Frequency domain
x
(
t
): continuous and periodic signals
X
(
Ω
): discrete and aperiodic CTFT
1
CTFT
←−−→
w
t
2
p
T
0
2
p
T
0
0
−
−2
T
0
−
T
0
0
T
0
2
T
0
(a)
x
(
t
): continuous and aperiodic signals
X
(
Ω
): Continuous and aperiodic CTFT
1
CTFT
←−−→
t
w
p
p
−
0
−
W
0
W
W
W
(b)
x
[
k
]: discrete and periodic signals
X
(
Ω
): discrete and periodic DTFT
DTFT
←−−→
W
k
−2
p
0
p
2
p
−
p
−8
−6
−4
−2
0
2
4
6
8
(c)
x
[
k
]: discrete and aperiodic signals
X
(
Ω
): continuous and periodic DTFT
1
1
1
DTFT
←−−→
k
W
−8
−6
−4
−2
0
2
4
6
8
−4
p
−2
p
0
2
p
4
p
(d)
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