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| − | 2. By adding up several cycles of the function <math>y(x)=x^2\!</math> we can turn a non-periodic signal into a periodic signal: | + | 2. By adding up several cycles of the function <math>y(x)=x^2\!</math> where <math>x=[0, 10]\!</math> we can turn a non-periodic signal into a periodic signal: |
[[Image:Xsquare_ECE301Fall2008mboutin.jpg]] | [[Image:Xsquare_ECE301Fall2008mboutin.jpg]] | ||
[[Image:Xsquare2_ECE301Fall2008mboutin.jpg]] | [[Image:Xsquare2_ECE301Fall2008mboutin.jpg]] | ||
Latest revision as of 09:10, 12 September 2008
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
$ 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 cycles of the function $ y(x)=x^2\! $ where $ x=[0, 10]\! $ we can turn a non-periodic signal into a periodic signal:
