Interesting Functions in Matlab

Douglas Wilhelm Harder, M.Math. LELDepartment 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.

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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

Interesting Functions in Matlab

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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