Digital Signal Processing Reference
In-Depth Information
9.17.
(a)
Determine which of the given signals are periodic:
(i) (ii)
(iii) (iv)
(v) (vi)
(b)
For those signals in part (a) that are periodic, determine the number of samples
per period.
x[n] = cos(pn)
x[n] =-3
sin(0.01pn)
x[n] = cos(3pn/2 + p)
x[n] = sin(3.15n)
x[n] = 1 + cos(pn/2)
x[n] = sin(3.15pn)
9.18.
In Figure P9.18, four discrete time sinusoids are plotted with labels Signal A, Signal B,
Signal C, and Signal D. Match these sinusoids to the signals
x
1
[n], x
2
[n],
x
3
[n] and x
4
[n].
(a)
(b)
(c)
(d)
x
4
[n] = 5 cos(
p
2
)
x
1
[n] = 5 cos(pn)
x
2
[n] = 5 sin(
p
2
)
x
3
[n] = 3 cos(2pn)
Signal A
Signal B
5
3
2.5
2
1.5
1
0.5
0
10
0
5
10
5
0
5
10
5
0
5
10
n
n
Signal C
Signal D
5
5
0
0
5
10
5
10
5
0
5
10
5
0
5
10
n
n
Figure P9.18
9.19.
Consider the signals shown in Figure P9.2.
(a)
Write an expression for
x
a
[n].
The expression will involve the sum of discrete im-
pulse functions.
(b)
Write an expression for
(c)
Write an expression for
(d)
Write an expression for
x
b
[n].
x
c
[n].
x
d
[n].
9.20.
(a)
Draw a block diagram, as in Figure 9.25, for a system described by
y
a
[n] = T(x[n]) = T
2
(x[n] + T
1
(x[n])) + T
3
(T
1
(x[n])).
