ECE 301, Homework #5, due date: 10/2/2008
http://www.ece.purdue.edu/
∼
chihw/ECE301
08F.html
Question 1:
A practical question. Let
y
(
t
) be a continuoustime
moving average system
over the past 15 time units, such that
y
(
t
) =
1
15
Z
t
t

15
x
(
s
)
ds.
The above system has many applications, some of which are listed as follows.
•
A missile tracking system:
x
(
t
) is the measured position of the target vehicle at time
t
, which is generally corrupted by noise. By averaging over the past 15 seconds, the
noise level can be reduced.
•
Stock index analysis: The moving average is important for stock index analysis,
which gives you the “average” performance of a particular stock in the past 15 days.
Answer the following questions:
1. Is the moving average an LTI system? Why?
2. What is the impulse response
h
(
t
)?
3. Is the moving average system memoryless? Stable? Causal? Invertible?
4. If the input signal is a sinusoidal wave
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 Spring '06
 V."Ragu"Balakrishnan
 Linear Algebra, Digital Signal Processing, LTI system theory

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