(→Non-Periodic Function) |
(→Non-Periodic Function) |
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<math> y = cos(n) </math> | <math> y = cos(n) </math> | ||
− | cos(n+N) for all n. N must be a multiple of 2*pi. | + | 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. | 2*pi is not an integer, but N must be an integer in order to be periodic. | ||
Therefore, y = cos(n) is not periodic. | Therefore, y = cos(n) is not periodic. |
Revision as of 14:43, 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 = 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.