Latest revision as of 17:30, 5 September 2008

> 1.1 > 1.2 > 1.3 > 1.4 > 1.5

Periodic Functions

$e^{2i*\Pi*}$ is a periodic function since it has the form $e^{N*W_o*\Pi}$ , where $$ W_o = 1 and N = 2 $$

By definition, $e^{N*W_o*\Pi}$ is a periodic function if $\frac{W_o}{2*\Pi}$ is a rational number.

$\frac{W_o}{2*\Pi}$ using the above numbers, yields a result of $\frac{1}{2}$ which is a rational number.

$e^{200i}$ is not a periodic function since $\frac{W_o}{2*\Pi}$ yields $\frac{100}{\Pi}$ which is not a rational number.

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 >[[HW1.1 Allen Humphreys_ECE301Fall2008mboutin| 1.1]]  >[[HW1.2 Allen Humphreys_ECE301Fall2008mboutin| 1.2]] >[[HW1.3 Allen Humphreys_ECE301Fall2008mboutin| 1.3]] >[[HW1.4 Allen Humphreys_ECE301Fall2008mboutin| 1.4]] >[[HW1.5 Allen Humphreys_ECE301Fall2008mboutin| 1.5]]
-==Periodic Functions==
+=Periodic Functions=
+==Functions==
+=== Period Function ===
+<math>e^{2i*\Pi*}</math> is a periodic function since it has the form <math>e^{N*W_o*\Pi}</math>, where <math>W_o = 1 and N = 2</math>
+By definition, <math>e^{N*W_o*\Pi}</math> is a periodic function if <math>\frac{W_o}{2*\Pi}</math> is a rational number.
+<math>\frac{W_o}{2*\Pi}</math> using the above numbers, yields a result of <math>\frac{1}{2}</math> which is a rational number.
+=== Non-Period Function ===
+<math>e^{200i}</math> is not a periodic function since <math>\frac{W_o}{2*\Pi}</math> yields <math>\frac{100}{\Pi}</math> which is not a rational number.