(New page: == Periodic and Non-Periodic Functions == === Periodic Functions === A continuous time signal is periodic if there exists a value <math> T </math> such that <math> x(t + T) = x(t) </mat...) |
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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 discrete time signal is periodic if there exists a value <math> N </math> such that <math> X[n + N] = X[n] </math>. | A discrete time signal is periodic if there exists a value <math> N </math> such that <math> X[n + N] = X[n] </math>. | ||
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| + | As you can see in the graph, at time <math> t = 0 </math>, <math> x(t) = 0</math>. This occurs again at <math> t = 4/3\pi </math>, and again at <math> -4/3\pi </math>. | ||
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| + | [[Image:ECE301HW1_ECE301Fall2008mboutin.JPG]] | ||
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| + | === Non-Periodic Functions === | ||
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| + | Using the same equation as above in discrete time, <math> X[n] = sin(3/4*n) </math> does not produce a periodic function. | ||
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| + | In the graph below, the function seems to be merely a scattering of points and doesn't follow a periodic pattern (due to the irrationality of <math>\pi</math>). | ||
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| + | [[Image:ECE301HW1b_ECE301Fall2008mboutin.JPG]] | ||
Latest revision as of 06:22, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
Periodic Functions
A continuous time signal is periodic if there exists a value $ T $ such that $ x(t + T) = x(t) $.
A discrete time signal is periodic if there exists a value $ N $ such that $ X[n + N] = X[n] $.
As you can see in the graph, at time $ t = 0 $, $ x(t) = 0 $. This occurs again at $ t = 4/3\pi $, and again at $ -4/3\pi $.
Non-Periodic Functions
Using the same equation as above in discrete time, $ X[n] = sin(3/4*n) $ does not produce a periodic function.
In the graph below, the function seems to be merely a scattering of points and doesn't follow a periodic pattern (due to the irrationality of $ \pi $).
