ENEE 241 02*
HOMEWORK ASSIGNMENT 13
Due Tue 04/07
Problem 13A
The realvalued signal vector
s
has DFT
S
=
£
12
z
1

2
j
z
2
4

j
z
3
3 + 2
j
z
4

2

5
j
/
T
(i) (2 pts.)
What are the values of
z
1
,
z
2
,
z
3
and
z
4
?
(ii) (3 pts.)
Without using complex algebra (or MATLAB), determine the sum of the entries of
s
.
(iii) (4 pts.)
Display the amplitude (

S
[
k
]

) and phase (
∠
S
[
k
]) spectra as vectors.
(iv) (7 pts.)
Write an equation for
s
[
n
] (where
n
= 0 : 8) in the form of a constant plus three
realvalued sinusoids with frequencies between 0 and
π
.
(v) (4 pts.)
In MATLAB, generate the vector
s
given by the equation found in part (iv) and
verify that
fft(s)
agrees with
S
.
Problem 13B
The signal vector
s
is given by
s
=
£
a b c d e f g h
/
T
(i) (8 pts.)
Display the following vectors:
•
s
(1)
=
s

Rs
•
s
(2)
=
P
2
s
+
P

2
s
•
s
(3)
=
F
4
Rs
•
s
(4)
=
Fs
+
F

1
s
(ii) (12 pts.)
Express the following vectors in terms of
P
,
R
,
F
and
s
:
•
s
(5)
=
£
2
a b
+
h c
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 Spring '08
 staff
 pts, 2 pts, Vector Motors, Konrad Zuse, BMW Z3, realvalued signal

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