(New page: ==Periodic Signals Revisited== The function chosen (by randomly clicking a name) from hw1 is y=sin(t). Found here: http://cobweb.ecn.purdue.edu/~mboutin/ECE301/Index.html) |
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The function chosen (by randomly clicking a name) from hw1 is y=sin(t). | The function chosen (by randomly clicking a name) from hw1 is y=sin(t). | ||
Found here: http://cobweb.ecn.purdue.edu/~mboutin/ECE301/Index.html | Found here: http://cobweb.ecn.purdue.edu/~mboutin/ECE301/Index.html | ||
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| + | I chose to modify the signal a bit and make it y = sin(5t). | ||
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| + | [[Image:sin5t_ECE301Fall2008mboutin.png]] | ||
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| + | :If you plot the signal in DT sampling at 5Hz you get a non-periodic signal as follows: | ||
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| + | [[Image:sin5tnonper_ECE301Fall2008mboutin.png]] | ||
| + | :It looks very close to periodic, but it does not follow the definition of x(n+N) = x(n) that was learned in class. However, there are no integer values that can be used to sample this function to create a periodic function in DT. | ||
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| + | :One can use <math> pi/3 </math> to sample the function and create a periodic signal. | ||
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| + | [[Image:sin5tper_ECE301Fall2008mboutin.png]] | ||
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| + | ==Part 2== | ||
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| + | We can take a non-periodic signal <math> y(t) = exp(t) </math> and shift it an infinite number of times periodically to create a periodic signal. | ||
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| + | [[Image:PeriExp_ECE301Fall2008mboutin.png]] | ||
Latest revision as of 09:22, 11 September 2008
Periodic Signals Revisited
The function chosen (by randomly clicking a name) from hw1 is y=sin(t). Found here: http://cobweb.ecn.purdue.edu/~mboutin/ECE301/Index.html
I chose to modify the signal a bit and make it y = sin(5t).
- If you plot the signal in DT sampling at 5Hz you get a non-periodic signal as follows:
- It looks very close to periodic, but it does not follow the definition of x(n+N) = x(n) that was learned in class. However, there are no integer values that can be used to sample this function to create a periodic function in DT.
- One can use $ pi/3 $ to sample the function and create a periodic signal.
Part 2
We can take a non-periodic signal $ y(t) = exp(t) $ and shift it an infinite number of times periodically to create a periodic signal.
