(Non-Periodic Functions)
 
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= Periodic versus non-periodic function=
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As part of the [[Homework_1_ECE301Fall2008mboutin|first homework]] in [[ECE301]] this semester, we were asked to give an example of a periodic function as well as an example of a non-periodic function. Here are my answers. A precise definition of periodic function can be found on my colleague [[HW1.4_Brian_Thomas_-_Periodic_Versus_Non-Periodic_Signals_in_Discrete_Time_ECE301Fall2008mboutin|Brian Thomas' page]]. An animated example can be found on [[HW1.4_Ben_Laskowski_-_Periodic_and_Non-Periodic_Functions_ECE301Fall2008mboutin|this page]].
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<span style="color:green"> Read the instructor's comments [[hw1periodicECE301f08profcomments|here]]. </span>
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== Periodic Functions ==
 
== Periodic Functions ==
 
A periodic function is a function which repeats over a period of time. A good example of periodic functions are:
 
A periodic function is a function which repeats over a period of time. A good example of periodic functions are:
:*<math>\,y = sin(x)</math>
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:*<math>\,y = sin(t)</math>
[[Image:Oddsinx_ECE301Fall2008mboutin.gif]]
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[[Image:Oddsinx_ECE301Fall2008mboutin.gif|300px]]
:*<math>\,y = cos(x)</math>
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[[Image:Evencosx_ECE301Fall2008mboutin.gif]]
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As you can see, this function repeats itself with a period of <math>2\pi</math>
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:*<math>\,y = cos(t)</math>
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[[Image:Evencosx_ECE301Fall2008mboutin.gif|300px]]
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As you can see, this function repeats itself with a period of <math>2\pi</math>
  
 
== Non-Periodic Functions ==
 
== Non-Periodic Functions ==
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:*<math>\,y = e^x</math>
 
:*<math>\,y = e^x</math>
 
[[Image:Graph14_ECE301Fall2008mboutin.png]]
 
[[Image:Graph14_ECE301Fall2008mboutin.png]]
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[[Main_Page_ECE301Fall2008mboutin|Back to ECE301 Fall 2008, Prof. Boutin]]

Latest revision as of 07:10, 14 April 2010

Periodic versus non-periodic function

As part of the first homework in ECE301 this semester, we were asked to give an example of a periodic function as well as an example of a non-periodic function. Here are my answers. A precise definition of periodic function can be found on my colleague Brian Thomas' page. An animated example can be found on this page.

Read the instructor's comments here.

Periodic Functions

A periodic function is a function which repeats over a period of time. A good example of periodic functions are:

  • $ \,y = sin(t) $

Oddsinx ECE301Fall2008mboutin.gif

As you can see, this function repeats itself with a period of $ 2\pi $

  • $ \,y = cos(t) $

Evencosx ECE301Fall2008mboutin.gif

As you can see, this function repeats itself with a period of $ 2\pi $

Non-Periodic Functions

Non periodic functions don't repeat. A good example of non-periodic functions are:

  • $ \,y = x^2 $

Parabola ECE301Fall2008mboutin.gif

  • $ \,y = e^x $

Graph14 ECE301Fall2008mboutin.png


Back to ECE301 Fall 2008, Prof. Boutin

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