Homework 1_ECE301Fall2008mboutin

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Periodic Functions

Functions

Period Function

$ 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.

Non-Period Function

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