(→Periodic Function) |
(→Periodic Function) |
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| Line 10: | Line 10: | ||
| − | Example in | + | Example in DT |
| − | <math> y = | + | <math> y = j^n </math> |
| + | |||
| + | 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== | ==Non-Periodic Function== | ||
Revision as of 14:40, 4 September 2008
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 = sin(n) $
