EE 2200 / Spring 2009: Assignment Three
1
ECE 2200 / Spring 2009
TRANSFER FUNCTIONS
ASSIGNMENT THREE
1
1. For the following discretetime systems with input
x
and output
y
, you are to
determine if they are timeinvariant (or not) and if they are linear (or not). You
are to ﬁrst answer these questions analytically, and then, using Matlab, construct
experiments to support your answer that perform the tests shown in Figures 5
16 and 517 of McClellan, Schafer, and Yoder,
Signal Processing First
(Pearson
Prentice hall, 2003).
(a)
y
[
n
] =
x
[

n
]
(b)
y
[
n
] = cos(2
πfn
)
x
[
n
]
(c)
y
[
n
] =

x
[
n
]

2. Consider two linear and timeinvariant discretetime systems with impulse responses
h
1
and
h
2
.
(a) If they are connected in series so that the output of the system with impulse
response
h
1
is the input to
h
2
, the impulse response of the overall system is the
convolution of
h
1
and
h
2
. Write a Matlab script that conﬁrms this result for
h
1
= [1
,
2
,
3
,
4] and
h
2
= [5
,
6] for the input
x
[
n
] = [7
,
8
,
9
,
10]. Conﬁrm that
this result is not altered by reordering the cascade connection so the input
x
enters system
h
2
and its output is the input to
h
1
.
(b) If they are connected in parallel so that both receive the same input and the
outputs of the system with impulse response
h
1
is added to the output of
h
2
,
the impulse response of the overall system is the sum of
h
1
and
h
2
. Write a
Matlab script that conﬁrms this result for
h
1
= [10
,
9
,
8
,
7] and
h
2
= [6
,
5] for
the input
x
[
n
] = [4
,
3
,
2
,
1].
3. Consider the transfer function