Digital Signal Processing Reference
In-Depth Information
TABLE 4.3
Fourier Series for Common Signals
Name
1.
Waveform
C
0
C
k
, k
0
Comments
x
(
t
)
X
0
2
X
0
k
C
k
0,
k
even
Square
wave
0
j
T
0
0
T
0
t
X
0
2.
x
(
t
)
X
0
X
0
2
X
0
2
k
Sawtooth
j
T
0
0
T
0
2
T
0
t
3.
x
(
t
)
X
0
2
2
X
0
(
k
)
2
C
k
0,
k
even
X
0
Triangular
wave
T
0
0
T
0
t
4.
x
(
t
)
X
0
2
X
0
2
X
0
(4
k
2
Full-wave
rectified
1)
2
T
0
T
0
0
T
0
2
T
0
3
T
0
4
T
0
t
C
k
0,
k
odd, except
5.
x
(
t
)
X
0
X
0
X
0
X
0
4
Half-wave
rectified
C
1
j
(
k
2
1)
X
0
4
0
T
0
T
0
2
T
0
and
C
1
j
t
6.
x
(
t
)
X
0
TX
0
T
0
TX
0
T
0
Tk
0
Tk
0
Tk
Rectangular
wave
sinc
2
2
T
0
0
T
0
T
2
T
2
T
0
2
T
0
t
7.
x
(
t
)
X
0
T
0
X
0
T
0
X
0
X
0
X
0
X
0
Impulse
train
T
0
0
T
0
2
T
0
t
