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6.003:
Signals
and
Systems
6.003:
Signals
and
Systems
Z
Transform
February
23,
2010
Z
Transform
Z
transform
is
discretetime
analog
of
Laplace
transform.
Furthermore,
you
already
know
about
Z
transforms
(we
just
haven’t
called
them
Z
transforms)
!
Example:
Fibonacci
system
diﬀerence
equation
y
[
n
]=
x
[
n
]+
y
[
n
−
1]
+
y
[
n
−
2]
operator
expression
Y
=
X
+
R
Y
+
R
2
Y
Y
1
system
functional
=
X
1
−R−R
2
unitsample
response
h
[
n
]:
1
,
1
,
2
,
3
,
5
,
8
,
13
,
21
,
34
,
55
,
89
,...
Check
Yourself
Example:
Fibonacci
system
diﬀerence
equation
y
[
n
x
[
n
y
[
n
−
1]
+
y
[
n
−
2]
operator
expression
Y
=
X
+
R
Y
+
R
2
Y
Y
1
system
functional
=
X
1
2
unitsample
response
h
[
n
1
,
1
,
2
,
3
,
5
,
8
,
13
,
21
,
34
,
55
,
89
Y
n
=
h
[
n
]
R
X
n
What’s
the
relation
between
H
(
z
)
and
h
[
n
]
?
Lecture
6
February
23,
2010
Midterm
Examination
#1
Wednesday,
March
3,
7:309:30pm.
No
recitations
on
the
day
of
the
exam.
Coverage:
Representations
of
CT
and
DT
Systems
Lectures
1–7
Recitations
1–8
Homeworks
1–4
Homework
4
will
not
collected
or
graded.
Solutions
will
be
posted.
Closed
book:
1
page
of
notes
(
8
1
2
×
11
inches;
front
and
back).
Designed
as
1hour
exam;
two
hours
to
complete.
Review
sessions
during
open
oﬃce
hours.
Check
Yourself
Example:
Fibonacci
system
diﬀerence
equation
y
[
n
x
[
n
y
[
n
−
1]
+
y
[
n
−
2]
operator
expression
Y
=
X
+
R
Y
+
R
2
Y
system
functional
Y
X
=
1
1
2
unitsample
response
h
[
n
1
,
1
,
2
,
3
,
5
,
8
,
13
,
21
,
34
,
55
,
89
What
is
the
relation
between
system
functional
and
h
[
n
]
?
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This note was uploaded on 11/07/2011 for the course ELECTRICA 6.003 taught by Professor Staff during the Summer '10 term at MIT.
 Summer '10
 staff

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