Periodic Signals 2.6 2002/07/18 2006/08/02 14:46:41.780 GMT-5 Michael Haag mjhaag@rice.edu Justin Romberg jrom@rice.edu Prashant Singh prash@ece.rice.edu Michael Haag mjhaag@rice.edu Mariyah Poonawala mariyah@rice.edu Richard G. Baraniuk richb@rice.edu Justin Romberg jrom@rice.edu Matthew Hutchinson mhutch@rice.edu period periodic periodic function periodicity signal t-periodic This module defines a periodic function and describes the two common ways of thinking about a periodic signal. Recall that a periodic function is a function that repeats itself exactly after some given period, or cycle. We represent the definition of a periodic function mathematically as: f t f t m T m m where T 0 represents the period. Because of this, you may also see a signal referred to as a T-periodic signal. Any function that satisfies this equation is periodic. We can think of periodic functions (with period T) two different ways: #1) as functions on all of

Function over all of where f t 0 f t 0 T

#2) or, we can cut out all of the redundancy, and think of them as functions on an interval 0 T (or, more generally, a a T ). If we know the signal is T-periodic then all the information of the signal is captured by the above interval.

Remove the redundancy of the period function so that f t is undefined outside 0 T .

An aperiodic CT function f t does not repeat for any T ; i.e. there exists no T s.t. this equation holds. Question: DT definitions?

Continuous-Time

Discrete-Time

Note: Circular vs. Line