Periodic versus non-periodic functions (hw1, ECE301)

Read the instructor's comments here.

Here is an example of a periodic function:

$ y = j e^{j 10 t} $

    $  = j(\cos 10t + j \sin 10t) $

    $ = j \cos 10t - \sin 10t $

When t = 0, y = j. We know that $ \cos $ and $ \sin $ have the same values when evaluated at 0 and $ 2\pi $. So, $ 10t = 2\pi $ when $ t = \frac{\pi}{5} $. This is the fundamental period.

Here is an example of a non-periodic function:

$ e^{(-1+j)t} $

    $ = e^{-t}(\cos t + j \sin t) $

This funtion is not periodic because the $ e^{-t} $ term makes the function decay exponentially.