Department of Electrical Engineering
EE355L: Signal & Systems
Course Instructor: Dr. Sohaib Abdul Rehman Dated:
Lab Instructor: Tawahaa Ahmed Semester: 5th
Class: BSEE-18 Session: Fall-2020
Lab 5. Graphical Convolution using NI Elvis
Lab Marks Obtained
Name Roll No VIVA(5)
(10) Marks (15)
Checked on: _______________________________
Signature: _______________________________
Inspired by
Engineering Signal & Systems: HANDS-ON LAB with NI ELVIS
© Ed Doering
5.1 Introduction
Convolution describes the time-domain process by which a linear time invariant system responds
to an input signal. Knowledge of the system’s impulse response permits the system output to be
computed for any input signal shape.
In this lab project you will determine the impulse response of two first order systems given their
step responses, apply graphical convolution to calculate the system output for a non-standard
signal shape, and then compare your calculations to simulation and hardware.
5.2 Objectives
1. Determine the impulse response of a system given its step response.
2. Calculate the system output to a non-standard pulse shape.
3. Measure the system output in hardware.
4. Compare analytical and measured results.
5.3 Theory & Procedure
5.3.1 Theory
The step response of the systems (a) shown in figure 5.1 is given as follow.
𝑡
𝑦𝑠𝑡𝑒𝑝 𝐴 (𝑡) = (1 − 𝑒 −𝑅𝐶 ) 𝑢(𝑡) (5.1)
Similarly, the step response of the system (b) shown in figure 5.1 is given as follow.
𝑡
𝑦𝑠𝑡𝑒𝑝 𝐵 (𝑡) = (𝑒 −𝑅𝐶 ) 𝑢(𝑡) (5.2)
The impulse response h(t) for these systems can be find using the following equation.
𝑑𝑦𝑠𝑡𝑒𝑝
ℎ(𝑡) = (5.3)
𝑑𝑡
The output signal y(t) can be found by using input signal x(t) and impulse response of system
h(t) with the help of graphical convolution which is given as follow.
∞
𝑦(𝑡) = 𝑥(𝑡) ∗ ℎ(𝑡) = ∫−∞ 𝑥(𝜏) ℎ(𝑡 − 𝜏) (5.4)
2
Figure 5.1. Two systems of RC circuit for graphical convolution
5.3.2 Procedure
We will be doing this lab on NI Elvis boards. You have to assemble your given circuit on the
bread board of Elvis board. Then the input signal will be given by the AO 0 or AO 1 analog outputs of
the Elvis board. Output waveform would be checked by any of the analog input ports. You have to
generate your signal using “Arbitrary waveform generator” in NI Elvis launcher. Figure-5.2 will help
you to find your required block in NI Elvis launcher. You have to make your signal by going into
“waveform editor” in the arbitrary waveform generator window as shown in figure 5.3. The input
signal can be form by using “new segment” and “new components” in the waveform editor window
identified in figure 5.4. The output waveform will be analyzed in the oscilloscope from launcher.
Figure 5.2. NI Elvis Launcher
3
Figure 5.4. Arbitrary waveform generator
Figure 5 4. Waveform Editor
4
5.4 Lab Tasks
5.4.1 Task 1. (2 Marks)
In this task you have to find the impulse response hA(t) and hB(t) of the system (a) and (b)
using equations written in section 5.3 taking value of R=1Ω and C= 1 F.
5.4.2 Task 2. (5 Marks)
(a) In this task you have to use the impulse response hA(t) and hB(t) found in previous
task to mathematically find yA (t) and yB (t) if we have an input signal x(t) as shown
in figure 5.5.
(b) Now implement the circuits shown in figure 5.1 on breadboard and apply input signal
x(t) with amplitude A=5 and use oscilloscope in NI Elvis to see the output yA (t) and
yB (t). Add screenshots of your output signals in your lab manual.
(c) Compare the mathematically found output signals by plotting them in MATLAB and
practically found signals and write your analysis in manual.
Figure 5.5. Input Signal x1 (t)
5.4.3 Task 3. (3 Marks)
(a) Evaluate yA (t) in both MATLAB and NI ELVIS at points 2, 4 and 6. Also compare
both plots at these points. What is the percentage error in practical and theoretical
value? Write your analysis in lab manual.
(b) Evaluate yB (t) in both MATLAB and NI ELVIS at points 2, 4 and 6. Also compare
both plots at these points. What is the percentage error in practical and theoretical
value? Write your analysis in lab manual.
