Digital Signal Processing Reference
In-Depth Information
sin(t)
sin(2t)
1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
0
100
200
300
400
500
600
700
t
Figure P4.6
4.7.
(a)
Find all integer values of
m
and
n
such that
cos
mv
0
t
and
cos
nv
0
t
are orthogonal
over the range where
(b)
Find all integer values of
m
and
n
such that
T
0
,
v
0
= 2p/T
0
.
cos
mv
0
t
and
sin nv
0
t
are orthogonal
over the range
(c)
Find all integer values of
m
and
n
such that
T
0
.
sin mv
0
t
and
sin nv
0
t
are orthogonal
over the range
T
0
.
4.8.
Find the combined trigonometric form of the Fourier series for the following signals in
Table 4.3:
(a)
Square wave
(b)
Sawtooth wave
(c)
Triangular wave
(d)
Rectangular wave
(e)
Full-wave rectified wave
(f)
Half-wave rectified wave
(g)
Impulse train
4.9.
Use (4.23) and the integral tables in Appendix A to verify the Fourier coefficients for
the following signals in Table 4.3:
(a)
Square wave
(b)
Sawtooth wave
(c)
Triangular wave
(d)
Rectangular wave
(e)
Full-wave rectified wave
(f)
Half-wave rectified wave
(g)
Impulse train
