Revision as of 09:12, 5 September 2008 by Jmazzei (Talk)

Periodic Functions

A Continuous Time signal is said to be periodic if there exists $ T > 0 $ such that $ x(t+T)=x(t) $

A Discrete Time signal is said to be periodic if there exists $ N > 0 $ (where N is an integer) such that $ x[n+N]=x[n] $

An example of a DT periodic signal is $ x[n] = j^{n} $ because

$ x[1] = j $

$ x[2] = -1 $

$ x[3] = -j $

$ x[4] = 1 $

$ x[5] = j $

$ x[6] = -1 $

$ x[7] = -j $

$ x[8] = 1 $

As you can see the function has a fundamental period of 4. Therefore any multiple of 4 is a period.

Non-periodic Functions

A Continuous Time signal is said to be non-periodic if there is no value of $ T > 0 $ that satisfies $ x(t+T)=x(t) $

A Discrete Time signal is said to be non-periodic if there is no value of $ N > 0 $ (where N is an integer) that satisfies$ x[n+N]=x[n] $

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood