(New page: A system x(t) (Continuous Time) is periodic if T>0 such that x(T+t) = x(t). A system x[n] (Discrete Time) is periodic if there exists N integer>0 such that x[n+N] = x[n] Not all complex e...) |
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Here is an example of a periodic system: | Here is an example of a periodic system: | ||
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| − | e^ | + | <math>e^{\frac{1}{4}j*\pi*n}</math> is periodic because: |
| − | wo=(1 | + | <math>wo=(\frac{1}{4}\pi)</math>, <math>\frac{wo}{2\pi}=\frac{1}{8}</math> which is a rational number |
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Here is an example of a non-periodic system: | Here is an example of a non-periodic system: | ||
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| − | e^ | + | <math>e^{\sqrt{3}j*\pi*n}</math> is not periodic because: |
| − | wo= | + | <math>wo=\sqrt{3}\pi</math> , <math>\frac{wo}{2\pi} = \frac{\sqrt{3}}{2}</math> which is not a rational number |
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Revision as of 11:02, 5 September 2008
A system x(t) (Continuous Time) is periodic if T>0 such that x(T+t) = x(t). A system x[n] (Discrete Time) is periodic if there exists N integer>0 such that x[n+N] = x[n]
Not all complex exponentials are periodic.
Here is an example of a periodic system:
$ e^{\frac{1}{4}j*\pi*n} $ is periodic because: $ wo=(\frac{1}{4}\pi) $, $ \frac{wo}{2\pi}=\frac{1}{8} $ which is a rational number
Here is an example of a non-periodic system:
$ e^{\sqrt{3}j*\pi*n} $ is not periodic because: $ wo=\sqrt{3}\pi $ , $ \frac{wo}{2\pi} = \frac{\sqrt{3}}{2} $ which is not a rational number
