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Barrett  CS450 Winter 2011
Lecture 1011
http://www.jhu.edu/signals/convolve/
)
1.
Linear shiftinvariant systems:
• What is the
superposition
principle? The multiplicative property? The additive property?
Show it graphically. Show it mathematically.
• Is the system
y
(
n
) =
nx
(
n
) linear? Is the system
y
(
n
) =
Ax
(
n
) +
B
linear?
• What is shiftinvariance? Show it graphically. Show it mathematically.
• In a particular system,
Π
(
π
t
) >
cosech
(2
t
) and
(
(
ta
)) >
cosech
(2
πα
t
). Is the system shiftinvariant?
• What is a Dirac delta function (Impulse)? Define it graphically and mathematically.
• Define the “impulse response” of a system.
• Why is the impulse response important in terms of being able to
characterize
a system.
2.
Harmonic Functions
• How do we represent harmonic functions (sines and cosines) as complex exponentials?
• What is the transfer function
K
(
ω
)? Is it dependent or independent of space/time 
and why is this significant in terms of being able to
characterize
a system using
K
(
ω
)?
• If I input a harmonic signal into a system, will it always produce a harmonic output?
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 Winter '08
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