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EE 242 Signal Processing I Winter 2022 Quiz 2
发布时间:2022-04-26
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Department of Electrical and Computer Engineering
Winter 2022 - EE 242 Signal Processing I
Quiz 2
Problem 1 (10pts)
Suppose that a discrete-time linear system has output y[n] for the given input x[n] as shown in Figure 1andFigure 2.
Linear |
|
Find
4 [
] given
4 [
] shown below. Show your work (hint: superposition)
4 [
]
1
Linear |
- 1
b) Determine whether the system is time-invariant. (Mathematical derivation for positive proof or counter example for a negative one)
Problem 2 (10pts)
For each part of the problem find the expression for and graph (
) if ℎ(
) =
−
(
).
a) 1 (
) =
(
)
b) 2 (
) =
2
1 3
Problem 3 (10pts)
Discrete-time LTI systems. Consider a signal 1 [
] =
[
] −
[
− 4] and an LTI system T
with impulse response ℎ[] =
[
]
Answer the following questions about the system T, as described by ℎ[] and justify your answer for each:
a) Memoryless?
b) Causal?
c) Stable?
Problem 4 (20pts)
Continuous-time Fourier Series and LTI systems
a) Consider an input signal (
) = 5 + 4 cos(3
) cos(2
) +
sin(2
) +
3
Find the Fourier Series representation (fundamental frequency
and coefficients
) of
(
) such that
(
) =
= −∞
b) Find (
) given
and the FS coefficients
that
= 6
= 4
= 1.7
= −2
= 3
5 = −3
Be sure to show
(
) as sinusoid when possible
Bonus Problem (5pts)
Find the Fourier series coefficients for each of the following signals.
a) (
) = [1 + cos(
)] [sin(6
−
)]
b) (
) = 5
(
− 3) (
(
) is from part a)