(New page: Here is an example of a periodic function: <math>y = j e^{j 10 t}</math> <math> = j(\cos 10t + j \sin 10t)</math> <math>= j \cos 10t - \sin 10t</math> When t = 0, y = j. We ...) |
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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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Here is an example of a periodic function: | Here is an example of a periodic function: | ||
Latest revision as of 07:25, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
Here is an example of a periodic function:
$ y = j e^{j 10 t} $
$ = j(\cos 10t + j \sin 10t) $
$ = j \cos 10t - \sin 10t $
When t = 0, y = j. We know that $ \cos $ and $ \sin $ have the same values when evaluated at 0 and $ 2\pi $. So, $ 10t = 2\pi $ when $ t = \frac{\pi}{5} $. This is the fundamental period.
Here is an example of a non-periodic function:
$ e^{(-1+j)t} $
$ = e^{-t}(\cos t + j \sin t) $
This funtion is not periodic because the $ e^{-t} $ term makes the function decay exponentially.
