ENEE 241 02*
HOMEWORK ASSIGNMENT 8
Due Tue 04/05
The MATLAB functions
OSHIFT
,
OFLIP
and
FDIAG
found in the Assignment 8 folder can be used
for circular shifts, circular reversals and products with Fourier sinusoids (by means of
F
). You may
use these functions to verify your results for Problem 8A. Copy these Mfiles to a local directory
and include that directory in the MATLAB path.
Problem 8A
Suppose the signal
s
=
a
b
c
d
e
f
g
h
T
of Problem 7C has DFT
S
=
4
1 + 2
j
5
3
j
−
7
−
3
j
5
1
−
2
j
T
Without computing any DFTs or inverse DFTs, determine (in numerical form) the DFTs of the
signal vectors
s
(1)
through
s
(7)
constructed in that problem.
Problem 8B
Let
x
be a
realvalued
vector of length
N
= 64 whose DFT
X
satisfies
X
[
k
]
= 0 for
k
= 0 : 13
and
X
[
k
] = 0 for
k
= 14 : 32
Explain your answers to
(i)
–
(v)
below.
(i) (4 pts.)
For what values of
k
between 33 and 63 does
X
[
k
] equal zero?
(ii) (4 pts.)
Let
x
(1)
[
n
] =
x
[
n
] cos(3
π
n/
8)
,
n
= 0 : 63
For what values of
k
does
X
(1)
[
k
] equal zero?
(iii) (4 pts.)
Let
x
(2)
=
P
4
x
+
P
−
4
x
For what values of
k
does
X
(2)
[
k
] equal zero?
(iv) (4 pts.)
Let
y
=
x
+
Rx
What is the imaginary part of the vector
Y
? Is it true that
Y
=
RY
?
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 Spring '08
 staff
 DFT, T

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