ELEC 320, Fall 2006
Profs. Wismer & Kozick
Matlab Tutorial, Convolution Computations,
and Convolution Applications
The objectives in lab this week are to learn more about Matlab and
to the convolution integral.
You will have a chance to practice performing the convolution
operation as well as see how it is applied to LTI system analysis.
Please work in pairs on these lab exercises.
Lab Reports: Each pair of
students is required to
submit a report explaining your answers to items 2 through 5.
This "report" can be hand-written, and is actually more like
a homework assignment.
The objective is for you to practice with convolution
computations, show all of the steps in your solutions,
and hear the effects of convolution on sound signals.
- You may find it helpful to refer to the MATLAB tutorial developed by
Professor Jim Maneval at
We recommend that you write a Matlab program to solve item 4 on
Homework 7, but it is not required that you
use Matlab for that assignment.
- Find the impulse response h(t) of an ideal integrator,
i.e. a system whose output y(t) is the integral of the input
as in .
- Convolve a unit step function with itself: y(t) = u(t) * u(t),
and sketch y(t).
- Consider the signals s1(t), s2(t) and
filters with impulse response h1(t), h2(t)
as shown below.
Compute the output of each filter due to each input.
That is, compute the four convolutions
y11(t) = s1(t) * h1(t),
y12(t) = s1(t) * h2(t),
y21(t) = s2(t) * h1(t),
y22(t) = s2(t) * h2(t).
These signals and filters are commonly used in digital
systems that transmit bits (0s and 1s) from one place to another.
- An application of convolution:
The MATLAB script
passes digitized music through discrete-time
systems with various impulse responses and then plays the resulting
Simulations of this type are used to understand how an
audio speaker or a listening room with a certain impulse response
will affect the music that is heard in the room.
The impulse response can be measured easily in practice in order
to obtain a model for a listening room.
Run the Matlab script mus.m.
You will also need to download the file
slove.au and save it in the same directory
The original music will be played, followed by the music convolved
g(t) = (2 pi 300) exp(-2 pi 300 t),
and then the music convolved with
a different function h(t).
The impulse responses
g(t) and h(t) will be plotted on your screen. The program takes
a while to run, so be patient!
You can listen to the results here, without running the MATLAB program:
Please write brief answers to the following questions.
You don't have to submit any plots.
- What effect does convolution with g(t) have on the music,
i.e. what is different about the music after the processing?
Can you explain this effect from the shape of g(t)?
(Hint: Does g(t) resemble the impulse response of an RC circuit?
What type of filter does g(t) describe, and what is the cutoff
- What effect does convolution with h(t) have on the music?
Can you relate this effect to the shape of h(t)? What
physical mechanism might give rise to an effect like this
in a concert hall?
All reports are due
at the beginning of your next lab meeting on
October 9 or 11.
Thank you, and have fun!