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As illustrated above, the function is clearly periodic, and has 4 as the smallest period. | As illustrated above, the function is clearly periodic, and has 4 as the smallest period. | ||
| − | On the other hand, <math>cos(n)</math> is not a periodic signal because there is no integer that is multple of <math>2 | + | On the other hand, <math>cos(n)</math> is not a periodic signal because there is no integer that is multple of <math>2\pi</math> and is an integer. |
Latest revision as of 06:13, 5 September 2008
The definition of a periodic DT signal is that there exists an integer N such that $ x[n+N] = x[n] $ for all $ n $.
For example, $ x[n] = j^n $ is periodic. One can show that:
$ x[1] = j\, $
$ x[2] = -1\, $
$ x[3] = -j\, $
$ x[4] = 1\, $
$ x[5] = j\, $
$ x[6] = -1\, $
$ x[7] = -j\, $
$ x[8] = 1\, $
As illustrated above, the function is clearly periodic, and has 4 as the smallest period.
On the other hand, $ cos(n) $ is not a periodic signal because there is no integer that is multple of $ 2\pi $ and is an integer.
