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== Periodic Functions == | == Periodic Functions == | ||
| − | A Continuous Time signal is said to be periodic if there exists <math>T > 0</math> such that <math>x(t+T)=x(t)</math> | + | A Continuous Time signal is said to be periodic if there exists <math>\ T > 0</math> such that <math>\ x(t+T)=x(t)</math> |
| − | A Discrete Time signal is said to be periodic if there exists <math>N > 0</math> (where N is an integer) such that <math>x[n+N]=x[n]</math> | + | A Discrete Time signal is said to be periodic if there exists <math>\ N > 0</math> (where N is an integer) such that <math>\ x[n+N]=x[n]</math> |
An example of a CT periodic signal is <math>x(t) = sawtooth(t)</math>: | An example of a CT periodic signal is <math>x(t) = sawtooth(t)</math>: | ||
Revision as of 10:48, 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.
