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| + | [[Category:ECE301]] | ||
| + | [[Category:periodicity]] | ||
| + | =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= | ||
| + | <span style="color:green"> Read the instructor's comments [[hw1periodicECE301f08profcomments|here]]. </span> | ||
| + | |||
== CT Periodic Fx == | == CT Periodic Fx == | ||
| − | <math>x(t)=e^j*t</math> | + | <math>x(t)=e^j*t</math> |
| + | |||
<math>e^j*t</math>---> <math>cos(t) + j*sin(t)</math> | <math>e^j*t</math>---> <math>cos(t) + j*sin(t)</math> | ||
| + | |||
| + | the real part is periodic along with the imaginary part | ||
== DT Periodic Fx == | == DT Periodic Fx == | ||
| + | <math>x[n]=e^(j*w*n)</math> | ||
| + | |||
| + | the value will be periodic as long as | ||
| + | |||
| + | <math>w/(2*pi) = K/N </math> | ||
| + | |||
| + | K is any integer | ||
| + | |||
== CT NON-Periodic Fx == | == CT NON-Periodic Fx == | ||
| − | = | + | <math>x(t)=x^2</math> |
| + | |||
| + | does not follow the rules for periodic signals | ||
Latest revision as of 06:25, 14 April 2010
Contents
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
CT Periodic Fx
$ x(t)=e^j*t $
$ e^j*t $---> $ cos(t) + j*sin(t) $
the real part is periodic along with the imaginary part
DT Periodic Fx
$ x[n]=e^(j*w*n) $
the value will be periodic as long as
$ w/(2*pi) = K/N $
K is any integer
CT NON-Periodic Fx
$ x(t)=x^2 $
does not follow the rules for periodic signals
