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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> | ||
| + | |||
==Periodic Function== | ==Periodic Function== | ||
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Example in DT | Example in DT | ||
| − | <math> y = | + | <math> y = cos(n) </math> |
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| + | cos(n+N) = cos(n) for all n. N must be a multiple of 2*pi. | ||
| + | 2*pi is not an integer, but N must be an integer in order to be periodic. | ||
| + | |||
| + | Therefore, y = cos(n) is not periodic. | ||
Latest revision as of 07:26, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
Periodic Function
x(t) is periodic if there exists:
T > 0 x(t+T) = x(t)
x[n] is periodic if there exists:
N > 0 x[n+N] = x[n]
Example in DT
$ y = j^n $
j^n has a period of 4.
n = 1: y = j n = 2: y = -1 n = 3: y = -j n = 4: y = 1 n = 5: y = j n = 6: y = -1 n = 7: y = -j n = 8: y = 1
Non-Periodic Function
Example in DT
$ y = cos(n) $
cos(n+N) = cos(n) for all n. N must be a multiple of 2*pi. 2*pi is not an integer, but N must be an integer in order to be periodic.
Therefore, y = cos(n) is not periodic.
