(New page: '''Peridic and Non Periodic Signals''' ''Defination :'' -if x(t)=x(t+T) for all values of t ,for some T not equal to zero,then x(t) is periodic with period T. -if x(n)=x(n+N) for all va...) |
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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]]. </span> | ||
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'''Peridic and Non Periodic Signals''' | '''Peridic and Non Periodic Signals''' | ||
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''Defination :'' | ''Defination :'' | ||
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-if x(t)=x(t+T) for all values of t ,for some T not equal to zero,then x(t) is periodic with period T. | -if x(t)=x(t+T) for all values of t ,for some T not equal to zero,then x(t) is periodic with period T. | ||
-if x(n)=x(n+N) for all values of n ,some integer N ,then x(n) is periodic with period N. | -if x(n)=x(n+N) for all values of n ,some integer N ,then x(n) is periodic with period N. | ||
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Example of a periodic signal | Example of a periodic signal | ||
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| + | Q) Is x[n]=j^n periodic ? | ||
| + | Ans) | ||
| + | fundamental period of signal N=4 | ||
x[1] = j | x[1] = j | ||
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period =4,8,16 ,all mulitples of 4. | period =4,8,16 ,all mulitples of 4. | ||
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| + | Therefore it is a periodic signal | ||
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Example of a non periodic signal. | Example of a non periodic signal. | ||
Latest revision as of 06:13, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
Peridic and Non Periodic Signals
Defination :
-if x(t)=x(t+T) for all values of t ,for some T not equal to zero,then x(t) is periodic with period T.
-if x(n)=x(n+N) for all values of n ,some integer N ,then x(n) is periodic with period N.
Example of a periodic signal
Q) Is x[n]=j^n periodic ?
Ans)
fundamental period of signal N=4
x[1] = j x[2] = -1 x[3] = -j x[4] = 1 x[5] = j x[6] = -1 x[7] = -j x[8] = 1
period =4,8,16 ,all mulitples of 4.
Therefore it is a periodic signal
Example of a non periodic signal.
q) Is cos(n) a periodic signal ?
- we want a integer N such that
cos (n+N) = cos (n) for all n
N is a multiple of 2*pi but since no integer multiple of 2*pi is an integer Therefore cos (n) is not periodic.
