6.6 MATLAB Laboratory Experiments on Convolution
Purpose: In this section we design two experiments dealing with continuous- and
discrete-time convolutions and their applications to linear continuous- and discrete-time
dynamic systems. The purpose of the first experiment is to present the convolution
operator, and to demonstrate some of its properties in both continuous- and discrete-time
domains. By writing and modifying the corresponding MATLAB programs, students will
master every step of the convolution process. In the second experiment, the convolution
method will be used to determine the zero-state responses of both continuous- and
discrete-time linear dynamic systems by using the famous formula that states that the
response of a linear system at rest due to an arbitrary input is the convolution of that
input with the system impulse response.
6.6.2. Convolution for Linear Dynamic Systems
In this experiment, students are required to use the convolution operator to find the system
zero-state response for both continuous- and discrete-time linear dynamic systems. MAT-
LAB programs developed for the convolution of two signals in the previous experiment
can be used in this experiment, subject to minor modifications.
Part 1. Continuous-Time Systems
The output of a linear continuous-time system at rest due to any input
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is given
by the convolution formula
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(6.33)
Consider the continuous-time system at rest represented by the differential equation
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Take
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and discretize integral (6.33) as given in (6.31) with
,
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. Use MATLAB
and the convolution procedure to find and plot
(a) the impulse response of the system;
(b) the step response of the system; and
(c) the system zero-state response due to the input
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.
For (b) and (c) use the MATLAB program from Section 6.5.
Verify the results obtained by using the MATLAB functions step and lsim.
Part 2. Discrete-Time Systems
Consider the discrete-time system represented by the difference equation
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