Digital Signal Processing Reference
In-Depth Information
x
(
t
)
1
1
1
• • •
• • •
0.1
0.1
0.3
0
0.2
0.2
t
1
1
1
Figure P4.14
(e)
Figure P4.11(e)
(f)
Figure P4.11(f)
Check your results, using Table 4.3.
4.18.
(a)
Sketch the frequency spectrum for the square wave of Table 4.3, for
(b)
Repeat part (a) for the sawtooth wave.
(c)
Repeat part (a) for the triangular wave.
(d)
Repeat part (a) for the full-wave rectified signal.
(e)
Repeat part (a) for the half-wave rectified signal.
(f)
Repeat part (a) for the rectangular wave.
(g)
Repeat part (a) for the impulse train.
X
0
= 10.
4.19.
(a)
Sketch the frequency spectrum for the signal of Figure P4.10(a), showing the dc
component and the first four harmonics.
(b)
Repeat part (a) for the signal of Figure P4.10(b).
(c)
Repeat part (a) for the signal of Figure P4.10(c).
(d)
Repeat part (a) for the signal of Figure P4.10(d).
(e)
Repeat part (a) for the signal of Figure P4.10(e).
(f)
Repeat Part (a) for the signal of Figure P4.10(f).
4.20.
(a)
Sketch the frequency spectrum for the signal of Figure P4.11(a), showing the dc
component and the first four harmonics.
(b)
Repeat part (a) for the signal of Figure P4.11(b).
(c)
Repeat part (a) for the signal of Figure P4.11(c).
2
e
j
4
,
2
e
-
j
4
,
1
1
4.21.
Given and find the signal
x
(
t
) with
these Fourier coefficients. This is an example of signal
synthesis
.
v
0
= p, C
0
= 2, C
1
= 1, C
3
=
C
-3
=
q
4.22.
Find the Fourier coefficients of
x(t) =©
k=-
q
, k even
[u(t - k) - u(t - 1 - k)].
q
4.23.
Given the periodic signal
x(t) =©
n=-
q
, n even
[u(t - 3n) - u(t - 3n - 1)],
(a)
find its fundamental frequency;
(b)
find the Fourier coefficients of the exponential form.
4.24.
Consider the system of Figure P4.24, with
10
s + 5
.
H(s) =
