Interesting Functions in Matlab
Douglas Wilhelm Harder, M.Math. LEL
Department of Electrical and Computer Engineering
University of Waterloo
Waterloo, Ontario, Canada
ece.uwaterloo.ca
dwharder@alumni.uwaterloo.ca
© 2012 by Douglas Wilhelm Harder. Some rights reserved.
Interesting Functions in Matlab
Outline
You are already familiar with trigonometric and
exponential functions
We will now look at:
–
–
–
–
square wave functions
saw-toothed wave functions
triangular pulses
the cardinal sine function
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Interesting Functions in Matlab
Square Wave Function
The square-wave function has a period of 2p and an be
thought of as follows: 
sin  x  sin  x   0

n

square  x     1
x  2np
 sin  x  sin  x   0

 
x = 0:0.0001:20;
plot( x, square( x ) )
ylim( [-1.2 1.2] )
square( 0 )
ans = 1
square( pi )
ans = -1
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Interesting Functions in Matlab
Saw-toothed Wave Functions
The default saw-toothed has a period of 2p and an be
thought of as follows:
sawtooth  x  
x = 0:0.0001:20;
plot( x, sawtooth( x ) )
ylim( [-1.2 1.2] )
sawtooth( 0 )
ans = -1
sawtooth( pi )
ans = -1
 x 
 2   1
p
 2p 
x
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Interesting Functions in Matlab
Saw-toothed Wave Functions
A second argument indicates what proportion into the
interval [0, 2p] the peak of the tooth appears
– The defualt is identical to sawtooth( x, 1 )
x = 0:0.0001:20;
plot( x, sawtooth( x, 0.5 ) )
ylim( [-1.2 1.2] )
0.5
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Interesting Functions in Matlab
Saw-toothed Wave Functions
The last interesting case has the parameter as 0:
sawtooth  x,0   1 
x = 0:0.0001:20;
plot( x, sawtooth( x, 0 ) )
ylim( [-1.2 1.2] )
square( 0 )
ans = 1
square( pi )
ans = -1
 x 
 2 
p
 2p 
x
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Interesting Functions in Matlab
The Cardinal Sine Function
The sinc function is not periodic and is defined as:
 1

sinc  x    sin p t 

 pt
x = -10:0.0001:10;
plot( x, sinc( x ) )
ylim( [-1.2 1.2] )
x0
x0
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Interesting Functions in Matlab
The Triangular Pulse Function
The triangular-pulse function is not periodic and is
defined as:
x  1
 0
x 1

tripuls  x   
1  x
 0
x = -2:0.0001:2;
plot( x, tripuls( x ) )
ylim( [-1.2 1.2] )
1  x  0
0  x 1
1 x
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Interesting Functions in Matlab
Summary
We have quickly covered some of the special functions
in Matlab
– square, sawtooth, tripuls and sinc
This will be used later in applications
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Interesting Functions in Matlab
References
[1]
Jack Little, Cleve Moler, and Steve Bangert, Matlab, Mathworks, 19842012.
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