(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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| + | =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= | ||
| + | <span style="color:green"> Read the instructor's comments [[hw1periodicECE301f08profcomments|here]]. </span> | ||
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A system x(t) (Continuous Time) is periodic if T>0 such that x(T+t) = x(t). | 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] | A system x[n] (Discrete Time) is periodic if there exists N integer>0 such that x[n+N] = x[n] | ||
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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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Latest revision as of 06:22, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
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
