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McGill University
Winter 2009
ECSE 304B
Prof. Jan Bajcsy
Assignment 5
Due date: April 14 at 16:00
TAs:
Mr. Daniel Kim, Sami elBaddagh, Yi Feng
1.
DiscreteTime Transforms
(a)
Find the
z
transform
X(z)
and sketch the region of convergence
for signal
x[n]
that is shown the
figure below:
6
4
2
0
2
4
6
8
1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
n
x[n]
(1/3)
n
(1/2)
n
(b)
Does the discretetime Fourier transform
(
)
j
X e
w
exist for the signal from part (a)? If yes,
determine
(
)
j
X e
explicitly, if not, explain why.
(c)
Repeat part (a) for signal
2
[ ]
(
1) [
]
y n
n
n
u
n
=

+

, where
u[.]
is the unit step function.
(d)
Repeat part (b) for the above signal
y[n]
.
2. DiscreteTime Systems
Consider a system that has its inputoutput relationship described by
[ ]
0.7 [
1] 0.3 [ ]
y n
y n
x n
=

+
and is initially at rest, i.e.,
y[n]=0
for very negative values of
n, n<<0.
(a)
Depict a schematic block diagram of this discretetime system using delay blocks, interconnects,
adders, multipliers, etc.
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This note was uploaded on 07/09/2011 for the course ECSE 304 taught by Professor Chenandbacsy during the Spring '11 term at McGill.
 Spring '11
 ChenandBacsy

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