EE 309 Signals and Systems Lab
Fall 2016
Lab 4: LTI System Sinusoidal Response
Learning Objectives:

Analyze the response of an LTI system to a sinusoidal input

Reinforce the fundamental property of linear systems in relationship to tones

Introduce the notion of high-pass and low-pass filters
Lab Overview:
One of the most fundamental properties of a LTI system is that the output can only contain frequencies
present in the input. Specifically, if a tone (i.e., single frequency sinusoidal signal) is input to a LTI system the
output will also be a tone of the same frequency, however, the amplitude and phase may change.
In this lab we will analyze and simulate the expected system response of two RC circuits (previously
introduced, in Lab 03) to individual tones and finally construct the circuits in order to measure their actual tonal
responses.
Grading:
Problem (value)
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Points Awarded
Task 1 (20 points)
0
Task 2 (10 points)
0
Questions 1 & 2 (10 points)
0
Task 3 (10 points)
0
Questions 3 & 4 (10 points)
0
Task 4 (10 points)
0
Questions 5 & 6 (10 points)
0
Task 5 (10 points)
0
Questions 7 & 8 (10 points)
0
Total (100 points)
0.00
Lab 04
Enter points per problem,
then, select the number in
Total and hit F9 to update
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EE 309 Signals and Systems Lab
Fall 2016
Experiments
EXPERIMENT 1.
ANALYSIS OF THE FREQUENCY RESPONSE OF THE TWO CIRCUITS
Figure 1 presents two RC circuits each with an input
x(t ) and output y (t ) .
i (t )
i (t )
Figure 1 Two RC circuits.
Task 1.
Analyze each of the two circuits to determine the frequency response function of each. Be sure
to show the steps of your analysis NOT just the final result.
Circuit (a) Frequency Response Function:
H a ()  ??
??
(1.1)
Hb ()  ??
??
(1.2)
Circuit (b) Frequency Response Function:
Task 2.
Selecting R  10 k  and C  100  F , use MATLAB to plot the magnitude of the frequency
response function (i.e., H ( ) ) of both systems vs frequency, for a frequency range of   0 to 4
rad/s (i.e., f  0 to 2 Hz) in Figure 2. Plot the frequency in Hz rather than radians/s.
Plot of Circuit (b) magnitude Response
Plot of Circuit (a) magnitude Response
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Lab 04
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EE 309 Signals and Systems Lab
Fall 2016
Figure 2 Magnitude response of two RC circuits.
Question 1. Considering circuit (a), at what frequency (in Hz) will the output signal be 20% the magnitude of
the input frequency? ___???______ Hz
Question 2. Considering circuit (b), at what frequency (in Hz) will the output signal be 80% the magnitude of
the input frequency? ___???______ Hz
Task 3.
Retaining the same capacitor and resistor values as above, use MATLAB to plot the phase
response (i.e.,
 H ()  ) of both systems vs frequency, for a frequency range of   0 to 4 rad/s (i.e.,
f  0 to 2 Hz) in Figure 2. Plot the frequency in Hz rather than radians/s and the phase in degrees
rather than radians.
Plot of Circuit (b) Phase Response
Plot of Circuit (a) Phase Response
Figure 3 Phase response of two RC circuits.
Question 3. At the frequency identified in Question 1, what should be the phase shift between the input and
output waveforms? ___???____ in Degrees
Question 4. At the frequency identified in Question 2, what should be the phase shift between the input and
output waveforms? ___???____ in Degrees
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EE 309 Signals and Systems Lab
EXPERIMENT 2.
Fall 2016
HARDWARE IMPLEMENTATION OF THE TONE RESPONSE OF THE TWO CIRCUITS
In this portion of the Lab you will be building circuits (a) and (b) as shown in Figure 1 with R  10 k  and
C  100  F . Use the provided MATLAB code (lab04.m) to apply a 1 V amplitude sinusoidal input (
x(t )  A Sin(2 ft ) , with A  1 and f  TBD ) and save both the input and the output signals to a mat file
(lab04_exp2_part_a.mat or lab04_exp2_part_b.mat).
Task 4.
Referring to circuit (a), apply a 1 V amplitude sinusoidal with the frequency you determined in
answering Question 1. Plot the hardware based sinusoidal response in Figure 4 for a 10 second interval.
Be sure to include BOTH the input and the output waveforms in each plot.
ZOOMED-IN VERSION of
Plot of Circuit (a) Response
Plot of Circuit (a) Response
Figure 4 Hardware based impulse response of circuit (a).
Question 5. Referring to Figure 4, what is the time shift between the input and output waveforms?
__????____ in seconds
Question 6. Referring to Figure 4, what is the phase shift between the input and output waveforms?
__????____ in Degrees
YOUR NAME(S)
Lab 04
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EE 309 Signals and Systems Lab
Task 5.
Fall 2016
Referring to circuit (b), apply a 1 V amplitude sinusoidal with the frequency you determined in
answering Question 2. Plot the hardware based sinusoidal response in Figure 5 for a 20 second interval.
Be sure to plot BOTH the input and the output waveforms.
ZOOMED-IN VERSION of
Plot of Circuit (b) Response
Plot of Circuit (b) Response
Figure 5 Hardware based impulse response of circuit (b).
Question 7. Referring to Figure 5, what is the time shift between the input and output waveforms?
__????____ in seconds
Question 8. Referring to Figure 5, what is the phase shift between the input and output waveforms?
__????____ in Degrees
YOUR NAME(S)
Lab 04
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EE 309 Signals and Systems Lab
Fall 2016
Appendices
APPENDIX A: MATLAB CODE FOR EXPERIMENT 1
APPENDIX B: MATLAB CODE FOR EXPERIMENT 2
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Lab 04
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