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For example, <math>x[n] = j^n</math> is periodic. One can show that: | For example, <math>x[n] = j^n</math> is periodic. One can show that: | ||
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<math>x[1] = j\,</math> | <math>x[1] = j\,</math> | ||
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| + | <math>x[2] = -1\,</math> | ||
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| + | |||
| + | <math>x[3] = -j\,</math> | ||
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| + | <math>x[4] = 1\,</math> | ||
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| + | <math>x[5] = j\,</math> | ||
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| + | <math>x[6] = -1\,</math> | ||
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| + | <math>x[7] = -j\,</math> | ||
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| + | |||
| + | <math>x[8] = 1\,</math> | ||
Revision as of 18:47, 4 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\, $
