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 [email protected] © 2012 by Douglas Wilhelm Harder. Some rights
Mar 31, 2015
Interesting Functions in Matlab
Douglas Wilhelm Harder, M.Math. LELDepartment of Electrical and Computer Engineering
University of Waterloo
Waterloo, Ontario, Canada
ece.uwaterloo.ca
© 2012 by Douglas Wilhelm Harder. Some rights reserved.
2
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
Interesting Functions in Matlab
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Square Wave Function
The square-wave function has a period of 2p and an be thought of as follows:
x = 0:0.0001:20;plot( x, square( x ) )ylim( [-1.2 1.2] )square( 0 ) ans = 1
square( pi ) ans = -1
sin sin 0
square 1 2
sin sin 0
n
x x
x x n
x x
Interesting Functions in Matlab
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Saw-toothed Wave Functions
The default saw-toothed has a period of 2p and an be thought of as follows:
x = 0:0.0001:20;plot( x, sawtooth( x ) )ylim( [-1.2 1.2] )sawtooth( 0 ) ans = -1sawtooth( pi ) ans = -1
sawtooth 2 12
x xx
Interesting Functions in Matlab
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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
Interesting Functions in Matlab
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Saw-toothed Wave Functions
The last interesting case has the parameter as 0:
x = 0:0.0001:20;plot( x, sawtooth( x, 0 ) )ylim( [-1.2 1.2] )square( 0 ) ans = 1square( pi ) ans = -1
sawtooth ,0 1 22
x xx
Interesting Functions in Matlab
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The Cardinal Sine Function
The sinc function is not periodic and is defined as:
x = -10:0.0001:10;plot( x, sinc( x ) )ylim( [-1.2 1.2] )
1 0
sinc sin0
x
x tx
t
Interesting Functions in Matlab
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The Triangular Pulse Function
The triangular-pulse function is not periodic and is defined as:
x = -2:0.0001:2;plot( x, tripuls( x ) )ylim( [-1.2 1.2] )
0 1
1 1 0tripuls
1 0 1
0 1
x
x xx
x x
x
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Summary
We have quickly covered some of the special functions in Matlab– square, sawtooth, tripuls and sinc
This will be used later in applications
Interesting Functions in Matlab
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References
[1] Jack Little, Cleve Moler, and Steve Bangert, Matlab, Mathworks, 1984-2012.
Interesting Functions in Matlab