Difference between revisions of "HW1.4 Joseph Mazzei ECE301Fall2008mboutin" - Rhea

Revision as of 09:42, 5 September 2008

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 CT periodic signal is $ x(t) = sawtooth(t) $:

As you can see the function has a fundamental period of two Pi. Therefore any multiple of two Pi 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] $

An example of a non-periodic continuous time signal would be $ \ x(t) = e^{(-1 + j)t} $. This goes to show that not all complex exponential functions are periodic.

Here is what the function looks like when graphed:

As you can see from the graph the function is non-periodic.