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Lab 1 for ECES 302
PiecewiseLinear Functions I
Background:
Many of the practical signals and input functions studied in our course are piecewisedefined
functions. Proficiency working with such functions in Matlab and Maple is critical if students are to have a rewarding
learning experience in the computer lab. The unit step function
u
(
t
) and the ramp function
r
(
t
) are the basic building
blocks needed to construct all piecewiselinear functions.
Exercise 1. Building Blocks for Piecewise Functions in Maple.
Here is how to define, evaluate and plot the units step function and ramp function in Maple.
> alias(u=Heaviside): r := t > t*u(t):
> u(2); u(0); u(2);
which returns:
0, undefined, 1
> r(2); r(0); r(2);
which returns:
0, undefined, 2
> plot( u(t), t = 2 .
. 2);
> plot( r(t), t = 2 .
. 2);
You can create a simultaneous plot of both using square bracket notation.
> plot( [u(t),r(t)], t = 2 .
. 2, color = [blue, red] );
The alias
command is used so
that students can enter the unit
step function as u(t) agreeing
with the notation in their book
and lectures, instead of having to
type out
Maple’s Heaviside
command each time. The ramp
function is defined as r(t) using
arrow notation.
Unit step
function u(t).
Ramp function r(t).
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function y = u(x)
y = ones( size(x) )/2;
set1 = find(x>0);
y(set1) = ones(size(set1));
set2 = find( x<0 );
y(set2) =zeros(size(set2))/2;
Below is an alternative version for u(x) which
would even work for matrices.
function y = r(x)
z = zeros( size(x) );
set1 = find( x>0 );
z(set1) = ones( size(set1) );
y=z.*x;
Below is an alternative version for r(x) which
would even work for matrices.
Exercise 2. Building Blocks for Piecewise Functions in Matlab.
W first need to create the unit step function and ramp function for use in Matlab. We will do this using mfiles.
In
Matlab, each function must be defined in a plain text file called an Mfile.
Open Matlab.
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 Spring '08
 CARR

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