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== Periodic Signals Revisited == | == Periodic Signals Revisited == | ||
| − | 1. By sampling at different frequencies the | + | 1. By sampling at different frequencies the signal <math>y=sin(x)\!</math> can appear as both periodic and non-periodic in DT. For example: |
<math>y(x)=sin(x) \!</math> in CT | <math>y(x)=sin(x) \!</math> in CT | ||
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The second graph has no integer value of N where y[n]=y[n+N], thus it is non-periodic. | The second graph has no integer value of N where y[n]=y[n+N], thus it is non-periodic. | ||
The third graph clearly shows there is an integer value of N where y[n]=y[n+N], thus it is periodic. | The third graph clearly shows there is an integer value of N where y[n]=y[n+N], thus it is periodic. | ||
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| + | <br> | ||
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| + | 2. By adding up several 10 unit cycles of the function <math>y(x)=x^2\!</math> we can turn a non-periodic signal into a periodic signal. | ||
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| + | [[Image:Xsquare_ECE301Fall2008mboutin.jpg]] | ||
| + | [[Image:Xsquare2_ECE301Fall2008mboutin.jpg]] | ||
Revision as of 19:28, 11 September 2008
Periodic Signals Revisited
1. By sampling at different frequencies the signal $ y=sin(x)\! $ can appear as both periodic and non-periodic in DT. For example:
$ y(x)=sin(x) \! $ in CT
$ y[n]=sin[n] \! $ with a sample rate of 1
$ y[n]=sin[n] \! $ with a sample rate of $ pi/4 \! $
The second graph has no integer value of N where y[n]=y[n+N], thus it is non-periodic.
The third graph clearly shows there is an integer value of N where y[n]=y[n+N], thus it is periodic.
2. By adding up several 10 unit cycles of the function $ y(x)=x^2\! $ we can turn a non-periodic signal into a periodic signal.
