ELEC2100 HW3
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ELEC2100 HW3
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Q.1 (16)
The block diagram of C/D and D/C system is shown below.
A CT signal
has bilateral bandwidth of 10 kHz and its frequency spectrum is shown below.
a) (2) What is the value of
(in rad/s) ?
If
is sampled using
where 50 .
b) (2) If the time duration of
is one second, specify the total number of sample points contained in
.
c) (2) Sketch the frequency spectrum of
. Show important values.
d) (2) Sketch the frequency spectrum of
for
|
|
3. Show important values.
The DT LTI system
is an ideal unity gain highpass filter with cutoff frequency of 0.2.
e) (2) Sketch the frequency spectrum of
for | |3. Show important values.
f) (2) Sketch the frequency spectrum of
. Show important values.
If the CT signal
is applied to the following system,
g) (2) Find FS coefficients of for 1,0,1.
h) (2) Sketch the frequency spectrum of
. Show important values.
DT LTI System
CT lowpass Filter
1
25s
…
…
t
50 0 50 100 (s)
(rad/s)
0
Q.2 (24)
The system function of a causal LTI system is given as
.
a) (2) Write down the differential equation relating the input
and the output
.
b) (2) Determine the output when the input is
is applied to
.
Another causal LTI system has the system function
.
c) (2) Sketch the polezero plot.
d) (2) Specify the ROC. Explain your answer.
e) (2) Is the system stable? Explain your answer.
f) (2) What is the value of the natural frequency of this system? What is the value of its zeta parameter ?
g) (2) Is the system oscillatory ? Explain your answer.
h) (2) Is the system overdamped, underdamped or critically damped ? Explain your answer.
i) (2) Specify the maximum gain, the halfpower gain and the halfpower frequency / frequencies.
j) (2) Roughly sketch the magnitude response. Show important values.
If an input
14sin
52
2sin
1000
is applied to this stable LTI system,
k) (2) Estimate the frequency response (in exponential form) at 0, 52 rad/s and 1000 rad/s.
l) (2) Represent the output
as the sum of real sine signals.