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| + | =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= | ||
| + | <span style="color:green"> Read the instructor's comments [[Hw1periodicECE301f08profcomments|here]] | ||
| + | |||
==Periodic Functions== | ==Periodic Functions== | ||
| − | The function <math>f(t)=sin(t | + | The function <math>f(t)=sin(t-T)</math> is periodic, with a period of <math>T=2\pi</math>. This means that for <math>T=2n\pi</math>, n an integer, the function will be unchanged from when <math>T=0</math>. |
| − | [[Image:Periodic_blaskows_ECE301Fall2008mboutin.gif|frame|center|An example of a periodic function <math>f(t)=sin(t | + | [[Image:Periodic_blaskows_ECE301Fall2008mboutin.gif|frame|center|An example of a periodic function <math>f(t)=sin(t-T)</math>. The dashed red line represents various values of <math>T</math> from <math>T=0</math> to <math>T=2\pi</math>. One can see that when <math>T=2\pi</math>, the function is unchanged.]] |
==Non-periodic Functions== | ==Non-periodic Functions== | ||
| − | A non-periodic function does not remain self-similar for all integer multiples of its period. A decaying exponential is an example of a non-periodic function. The distance between consecutive peaks does not remain constant for all values of <math>x</math>. Presented here is the function <math>f(t)=e^{0.2t}*sin(10t)</math>. | + | A non-periodic function does not remain self-similar for all integer multiples of its period. A decaying exponential is an example of a non-periodic function. The distance between consecutive peaks does not remain constant for all values of <math>x</math>, nor does the amplitude of consecutive peaks remain constant. Presented here is the function <math>f(t)=e^{0.2t}*sin(10t)</math>. |
| − | [[Image:Nonperiodic_blaskows_ECE301Fall2008mboutin.jpg|frame|center|An example of a non-periodic function <math>f(t)=e^{0.2t} | + | [[Image:Nonperiodic_blaskows_ECE301Fall2008mboutin.jpg|frame|center|An example of a non-periodic function <math>f(t)=e^{0.2t}sin(10t)</math>.]] |
Latest revision as of 07:09, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here
Periodic Functions
The function $ f(t)=sin(t-T) $ is periodic, with a period of $ T=2\pi $. This means that for $ T=2n\pi $, n an integer, the function will be unchanged from when $ T=0 $.
An example of a periodic function $ f(t)=sin(t-T) $. The dashed red line represents various values of $ T $ from $ T=0 $ to $ T=2\pi $. One can see that when $ T=2\pi $, the function is unchanged.
Non-periodic Functions
A non-periodic function does not remain self-similar for all integer multiples of its period. A decaying exponential is an example of a non-periodic function. The distance between consecutive peaks does not remain constant for all values of $ x $, nor does the amplitude of consecutive peaks remain constant. Presented here is the function $ f(t)=e^{0.2t}*sin(10t) $.
An example of a non-periodic function $ f(t)=e^{0.2t}sin(10t) $.
