P1/2
2012 Spring ELEC3100 Homework 2
(Deadline:26/03/2012 before 5pm)
Please submit your HW into the ELEC3100 HW Collection Box before 5pm on the deadline indicated
The HW collection box is located out of Rm2513.
Sampling
Q1. Consider a CT signal
t
t
t
t
t
x
π
144
cos
8
120
sin
4
24
cos
2
32
sin
3
)
(
+
+
−
=
.
(a). One engineer suggests to sample it at sampling frequency of 40 samples/sec to generate the sequence
x[n]. Determine the exact expression of x[n].
(b). Is the selection of sampling frequency reasonable? Can you correct it?
(c). What is the unit of the “ordinary frequency” for the CT signal? What is the unit of the “normalized digital
angular frequency” for the DT signal?
DFT
Q2. Let X[k] denote the DFT of x[n].
(a). Determine the values of X[k], 0
≤
k
≤
7, which is the 8
‐
point DFT of
)
N
/
n
2
cos(
]
n
[
x
π
=
for N=8 and 0
≤
n
≤
7.
(b). How many complex multiplications and complex additions are required for calculating each X[k]?
(c). What is the computation load for calculating DFT of x[n] in total?
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 Spring '13
 SONG
 CT signal, HW Collection Box, convolution outputs yL

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