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| − | + | [[Category:ECE301]] | |
| + | [[Category:periodicity]] | ||
| + | =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= | ||
| + | <span style="color:green"> Read the instructor's comments [[hw1periodicECE301f08profcomments|here]]. </span> | ||
| − | x[n]<math> | + | ==Periodic== |
| − | + | ||
| + | <math>x[n]=</math><math>j^{n}</math> is a discrete time (DT) periodic signal. It's period is 4*k, where k is an integer. However, it's fundamental period is 4. | ||
<math>j^{1}=-1</math> | <math>j^{1}=-1</math> | ||
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<math>j^{8}=j</math> | <math>j^{8}=j</math> | ||
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| + | ==Non-Periodic== | ||
| + | <math>x[n]=\cos{n}</math> is an example of a non-periodoc signal because there is not integer value for n such that <math>x[n+N]=x[n]</math>. It would be periodic if <math>N=K*2\pi</math>, but <math>\pi</math> is not an integer and therefore can not be chosen. | ||
Latest revision as of 06:24, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
Periodic
$ x[n]= $$ j^{n} $ is a discrete time (DT) periodic signal. It's period is 4*k, where k is an integer. However, it's fundamental period is 4.
$ j^{1}=-1 $
$ j^{2}=-j $
$ j^{3}=1 $
$ j^{4}=j $
$ j^{5}=-1 $
$ j^{6}=-j $
$ j^{7}=1 $
$ j^{8}=j $
Non-Periodic
$ x[n]=\cos{n} $ is an example of a non-periodoc signal because there is not integer value for n such that $ x[n+N]=x[n] $. It would be periodic if $ N=K*2\pi $, but $ \pi $ is not an integer and therefore can not be chosen.
