Latest revision as of 07:19, 14 April 2010

Periodic versus non-periodic functions (hw1, ECE301)

Read the instructor's comments here.

Functions are classified as periodic if there exists $T>0\!$ such that $y(x+T)=y(x)\!$ .

The following is an example of a periodic function:

y(x)=sin(pi*x)\!

This function is periodic because $y(x)=y(x+T)\!$ for $T=2, 4, 6\!$ etc.

Functions are classified as non-periodic if there exists no $T>0\!$ such that $y(x+T)=y(x)\!$ .

The following is an example of a non-periodic function:

y(x)=1/e^x\!

This function is not periodic because there exists no T where $y(x)=y(x+T)\!$ .

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+=Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])=
+<span style="color:green"> Read the instructor's comments [[hw1periodicECE301f08profcomments|here]]. </span>
 == Periodic Functions in Continuous Time ==
-* Functions are classified as periodic if there exists <math>T\!</math> such that <math>x(t+T)=x(t)\!</math>.
+* Functions are classified as periodic if there exists <math>T>0\!</math> such that <math>y(x+T)=y(x)\!</math>.
 <br>
 The following is an example of a periodic function:
@@ Line 8: / Line 11: @@
 <center>[[Image:Sinpix_ECE301Fall2008mboutin.jpg]]</center>
-When <math>x\!</math> is equal to 0,
+This function is periodic because <math>y(x)=y(x+T)\!</math> for <math>T=2, 4, 6\!</math> etc.
+== Non-Periodic Functions in Continuous Time ==
+* Functions are classified as non-periodic if there exists no <math>T>0\!</math> such that <math>y(x+T)=y(x)\!</math>.
+<br>
+The following is an example of a non-periodic function:
+<center><math>y(x)=1/e^x\!</math></center>
+<center>[[Image:Nonper_ECE301Fall2008mboutin.JPG]]</center>
+This function is not periodic because there exists no T where <math>y(x)=y(x+T)\!</math>.