Digital Signal Processing Reference
In-Depth Information
9.4.
The signals in Figure P9.2 are zero except as shown.
(a)
For the signal
x
a
[n]
of Figure P9.2(a), plot the following:
(i)
x
a
[-n]u[n]
(ii)
x
a
[n]u[-n]
(iii)
x
a
[n]u[n + 2]
(iv)
x
a
[-n]u[-2 - n]
(v)
x
a
[n]d[n - 2]
(vi)
x
a
[n](d[n + 1] + d[n - 1])
(b)
Repeat part (a) for the signal
x
b
[n]
of Figure P9.2(b).
(c)
Repeat part (a) for the signal
x
c
[n]
of Figure P9.2(c).
(d)
Repeat part (a) for the signal
x
d
[n]
of Figure P9.2(d).
9.5.
Given a signal
x[n] = 3(u[-n] - u[-n - 8]) + 6(u[n + 1] - u[n - 6]),
find and
plot
y[n] = x[-3n - 1].
9.6.
(a)
For the general case of transformations of discrete signals, given
x[n], x
t
[n]
can be
expressed as
x
t
[n] = Ax[an + n
0
] + B,
where
a
is rational and is an integer. Solve this expression for
x
[
n
].
(b)
Suppose that for the signal of Figure P9.6,
n
0
x
1
[n] = 1.5
x
3
[-n - 2] + 3.
Sketch
(c)
Verify the results of part (b) by checking at least three points in time.
x
3
[n].
x
1
[
n
]
x
2
[
n
]
4
2
2
1
•••
•••
•••
•••
12
3
2
1
3
n
4
3
2
1
0
1
2
n
2
Figure P9.6
9.7.
(a)
Find the even and odd parts of
x
1
[n]
in Figure P9.6.
(b)
Find the even and odd parts of
x
2
[n]
in Figure P9.6.
9.8.
(a)
Plot the even and odd parts of the signal of Figure P9.2(a).
(b)
Repeat part (a) for the signal of Figure P9.2(b).
(c)
Repeat part (a) for the signal of Figure P9.2(c).
(d)
Repeat part (a) for the signal of Figure P9.2(d).
9.9.
(a)
For each of the signals given, determine mathematically whether the signal is even,
odd, or neither.
(i)
x[n] = 6u[n - 3]
(ii)
x[n] =-n
x[n] = (.2)
ƒnƒ
x[n] = 6 + .2
n
+ .2
-n
(iii)
(iv)
(v)
x[n] = sin(2n)
(vi)
x[n] = sin(n - p/6)
