Revision as of 18:28, 11 September 2008 by Pjcannon (Talk)

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 Sinwave ECE301Fall2008mboutin.jpg

$ y[n]=sin[n] \! $ with a sample rate of 1 Samprate1 ECE301Fall2008mboutin.jpg

$ y[n]=sin[n] \! $ with a sample rate of $ pi/4 \! $ Samprate2 ECE301Fall2008mboutin.jpg


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.

Xsquare ECE301Fall2008mboutin.jpg Xsquare2 ECE301Fall2008mboutin.jpg

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