Homework 2_ECE301Fall2008mboutin - A - B - C - D - E

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 cycles of the function $ y(x)=x^2\! $ where $ x=[0, 10]\! $ we can turn a non-periodic signal into a periodic signal:

Xsquare ECE301Fall2008mboutin.jpg Xsquare2 ECE301Fall2008mboutin.jpg

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BSEE 2004, current Ph.D. student researching signal and image processing.

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