Revision as of 13:14, 11 September 2008 by Jkubasci (Talk)

Part 1

The function was chosen at random from HW1: HW1.4 Hang Zhang - Periodic vs Non-period Functions_ECE301Fall2008mboutin

$ \,x(t)=2cos(2\pi t)\, $


Periodic Signal in DT:

If $ x(t) $ is sampled at $ period=0.1 $, the function

$ \,y[n]=x[0.1n]=2cos(\frac{2\pi n}{10})\, $

would be periodic, since

$ \,y[n]=y[n+10N], \forall N\in Z\, $


This can be seen in the following plot (notice how the values lines up horizontally)

Jkubasci dt periodic ECE301Fall2008mboutin.jpg

Non-Periodic Signal in DT:

However, if $ x(t) $ is sampled at $ period=\frac{1}{2\pi} $, the function

$ \,z[n]=x[\frac{n}{2\pi }]=2cos(t)\, $

Part 2

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett