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Convolution for CT systems
We saw for DT systems:
 Definition of Impulse Response
h
[
n
]
 How TI & Linearity allow us to use
h
[
n
] to write an equation that gives the
output due to input
x
[
n
]
(That equation is Convolution)
CT LTI
ICs = 0
δ(
t
)
h
(
t
)
t
t
δ(
t
)
h
(
t
)
If system is causal
,
h
(
t
) = 0
for
t
< 0
The same ideas arise for CT systems!
(And the arguments to get there are very similar … so we won’t go into as much
detail!!)
Impulse Response
:
h
(
t
) is what “comes out” when δ(
t
) “goes in”
These overheads were originally developed by Mark Fowler at Binghamton University,
State University of New York.
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In what form will we know
h
(
t
)?
Our focus
is here
1.
h
(
t
) known analytically as a function
e.g.
h
(
t
) =
e
2
t
u
(
t
)
2. We may only have experimentally obtained samples:

h
(
nT
) at
n
= 0, 1, 2, 3, … ,
N
1
Now we can…
Use
h
(
t
) to find the zerostate response of the system for an input
h
(
t
)
x
(
t
)
y
(
t
)
CT LTI
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This note was uploaded on 02/01/2011 for the course ECE 3TP4 taught by Professor Drterrencetodd during the Fall '10 term at McMaster University.
 Fall '10
 DRTERRENCETODD

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