ELEG333
Signals and Systems
Final Exam
Spring 2020
Note:
The exam is open book, open notes. You can use any help you need except the help of another person (directly or indirectly).
The exam has to be uploaded on canvas by Friday, May 8, 10 AM. Exams submitted after this time will lose 5 points per hour (late). File can be uploaded only in word/ pdf format.
There will be a help session on Wednesday (5/6/20) from 10 am – 11 am on Zoom. Bring your questions there.
Label all graphs and write a short description of the plot below each plot describing what you are observing. Presentation of plots count!
Problem 1
Two separate recordings of equal length are made of a periodic pulse train being transmitted down a noisy channel. The following table shows the recorded values of the sampled voltages. Determine the amount of lag between the two recordings and the period of the waveform. You can use MATLAB for this problem. Use Cross-correlation (or any other technique) to get your answer. Attach the plots (graphs).
Record 1:
6.02
-5.98
7.92
-7.96
-0.78
-8.34
9.22
-2.65
-3.7
9.51
5.53
3.5
-3.18
-8.85
8.21
1.69
-0.06
6.65
-8.00
-9.21
-0.78
7.27
-5.98
-3.97
9.11
4.23
2.99
-1.85
-5.27
3.81
6.62
-2.64
2.08
-5.91
-3.58
-1.65
3.64
-8.19
-3.50
4.84
7.25
2.93
-4.42
-8.21
3.61
Record 2:
8.93
-7.20
-0.82
3.23
1.44
5.43
-9.88
-1.13
0.79
9.83
-8.73
4.64
-8.49
-4.66
-8.84
5.55
-8.24
-0.37
2.71
4.63
1.88
-0.92
-5.33
9.01
9.23
-3.70
5.08
-0.72
-5.08
-2.60
9.67
-8.55
-3.08
4.18
8.11
0.74
-3.87
-4.09
8.03
6.91
-9.87
-3.62
-8.29
-5.80
-7.04
Problem 2
The desired amplitude response of a certain band-pass FIR filter can be stated as:
H(f) =
1 for 250 ( f ( 750 Hz
=
0 elsewhere
The sampling rate is 2 KHz, and the order of the filter should be N = 15. Using FIR1 command in MATLAB, generate the 16 coefficients. Plot the frequency response of the filter to verify that it satisfies the specifications. Look and comment on both the phase and magnitude plot. Attach the program (commands) and plots.
Generate a signal:
x = 2*cos(0.1*pi*n) +3*sin(0.5*pi*n) + 2*cos(0.9*pi*n); (use n = 0:1000)
Assume sampling frequency Fs = 2000 Hz
Plot this signal in time domain and frequency domain.
Find the frequencies of the peaks in the frequency domain plot.
Now filter the signal x using the command:
y = filter(B, 1, x);
Plot this signal in time and frequency domain
Find the frequency of the peak in the frequency domain.
Did the filter work?
Problem 3.
A digital signal contains two frequency components: 1 = 0.1, and 2 = 0.2; the different components have amplitudes a1 = 1 and a2 = 5.
a) Generate such a sequence, which contains 1000 points (exactly 1000 points); plot the first 100; can you identify two distinct frequencies?
b) If you were to calculate the 1000-point FFT, X(k), at what values of k would these frequency components appear? Show your calculations.
c) Use Matlab to calculate and plot (magnitude of the) the 1000 point FFT (plot only the first .
ELEG333Signals and SystemsFinal ExamSpring 2020Note.docx
1. ELEG333
Signals and Systems
Final Exam
Spring 2020
Note:
The exam is open book, open notes. You can use any help you
need except the help of another person (directly or indirectly).
The exam has to be uploaded on canvas by Friday, May 8, 10
AM. Exams submitted after this time will lose 5 points per hour
(late). File can be uploaded only in word/ pdf format.
There will be a help session on Wednesday (5/6/20) from 10 am
– 11 am on Zoom. Bring your questions there.
Label all graphs and write a short description of the plot below
each plot describing what you are observing. Presentation of
plots count!
Problem 1
Two separate recordings of equal length are made of a periodic
pulse train being transmitted down a noisy channel. The
following table shows the recorded values of the sampled
voltages. Determine the amount of lag between the two
recordings and the period of the waveform. You can use
MATLAB for this problem. Use Cross-correlation (or any other
technique) to get your answer. Attach the plots (graphs).
Record 1:
6.02
-5.98
7.92
5. 0 elsewhere
The sampling rate is 2 KHz, and the order of the filter should be
N = 15. Using FIR1 command in MATLAB, generate the 16
coefficients. Plot the frequency response of the filter to verify
that it satisfies the specifications. Look and comment on both
the phase and magnitude plot. Attach the program (commands)
and plots.
Generate a signal:
x = 2*cos(0.1*pi*n) +3*sin(0.5*pi*n) + 2*cos(0.9*pi*n); (use n
= 0:1000)
Assume sampling frequency Fs = 2000 Hz
Plot this signal in time domain and frequency domain.
Find the frequencies of the peaks in the frequency domain plot.
Now filter the signal x using the command:
y = filter(B, 1, x);
Plot this signal in time and frequency domain
Find the frequency of the peak in the frequency domain.
Did the filter work?
Problem 3.
amplitudes a1 = 1 and a2 = 5.
a) Generate such a sequence, which contains 1000 points
(exactly 1000 points); plot the first 100; can you identify two
6. distinct frequencies?
b) If you were to calculate the 1000-point FFT, X(k), at what
values of k would these frequency components appear? Show
your calculations.
c) Use Matlab to calculate and plot (magnitude of the) the 1000
point FFT (plot only the first 500 points, since the rest are
redundant); do the frequencies appear at predicted locations?
Problem 4
Re-
problems?
Problem 5
Re-
primary difference between this
problem and the previous ones?
Problem 6
For the following filter specifications:
Gain > - -
(a) Design a butterworth filter. Write down the order and
coefficients of this filter. Check the corner frequencies using
the “freqz” command to see if the filter satisfies the
specifications.
(b) Design a ChevyshevI filter. Write down the order and
coefficients of this filter. Check the corner frequencies using
the “freqz” command to see if the filter satisfies the
specifications.
(c) Design an elliptical filter. Write down the order and
coefficients of this filter. Check the corner frequencies using
the “freqz” command to see if the filter satisfies the
specifications.
7. (d) Compare the three filters in (a), (b) and (c). Comment on the
differences (both magnitude and phase responses).
Show all commands used and attach all plots. Label all plots.
