ECSE 304 Signals and Systems 2
Online Quiz #1 Solutions
1. What is the fundamental period of the following DT signal?
x[n] = cos(pi*n/4) + sin(2*pi*n/6)
a)
24
b)
6
c)
12
d)
48
Solution
:
The fundamental periods of cos(pi*n/4) and sin(2*pi*n/6) are N = 8 and N = 3,
respectively. Thus, the fundamental period for their linear combination is N = 24.
2.
Is the signal
( )
⎟
⎠
⎞
⎜
⎝
⎛
+
=
−
n
j
n
x
n
8
2
cos
]
[
2
π
periodic?
If so, determine the fundamental
period.
( )
,...}
1
,
,
1
,
,
1
{
j
j
j
n
−
−
−
=
−
is periodic with period
N
= 4.
⎟
⎠
⎞
⎜
⎝
⎛
+
=
⎟
⎠
⎞
⎜
⎝
⎛
n
n
4
2
cos
2
1
2
1
8
2
cos
2
π
π
is periodic with period
N
= 4
Thus,
x
[
n
] is periodic with
fundamental period
N
= 4.
3.
Identify the appropriate Fourier representation for the following signal:

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