(Periodic Signals Revisited)
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[[Homework 2_ECE301Fall2008mboutin]] - [[HW2-A Phil Cannon_ECE301Fall2008mboutin|'''A''']] - [[HW2-B Phil Cannon_ECE301Fall2008mboutin|'''B''']] - [[HW2-C Phil Cannon_ECE301Fall2008mboutin|'''C''']] - [[HW2-D Phil Cannon_ECE301Fall2008mboutin|'''D''']] - [[HW2-E Phil Cannon_ECE301Fall2008mboutin|'''E''']]
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== Periodic Signals Revisited ==
 
== Periodic Signals Revisited ==
 
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:
 
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:
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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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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 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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