Lecture 4 problems
1.
For each system
: [
]
[
]
F
→
→
→
Z
R
Z
R
described below, determine which of
any of the following properties each system possesses.
(I)
Linearity;
(II)
Time invariance.
Explaining your reasoning clearly, but succinctly.
(a)
2
(
)
(
),
y n
x n
n
=
2200 ∈
Z
(b)
(
)
cos( (
)),
y n
x n
n
=
2200 ∈
Z
2. Consider a continuous-time system
F
→
→
→
¡
R
C
R
: [
]
[
]
having input signal
x and output signal y, as shown below:
This system takes the real part of its input signal:
(
)
Re(
)
y
F x
x
=
=
For each part below, you must explain your reasoning succinctly, but clearly and
convincingly.
(a)
Select the strongest true assertion from the list below:
(I)
The system must be time-invariant.
(II)
The system could be time-invariant, but does not have to be.
(III)
The system can not be time-invariant.
(b) Select the strongest true assertion from the list below:
(I)
The system must be linear.
(II)
The system could be linear, but does not have to be.
(III)
The system can not be linear.
3. The down sampler (decimator) system is as shown below:
(
)
(
)
y n
x nN
=
(a)
Is the down sampler linear?

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