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| − | By inspection, this function is non-periodic, as there is no <math>\,T\,</math> such that <math>\,y(t+T)=y(t)\,</math>. | + | By inspection, this function is non-periodic, as there is no <math>\,T\,</math> such that <math>\,y(t+T)=y(t)\,</math>. (The function is simply alternating between <math>\,e^{\frac{-t}{5}}\,</math> and <math>\,-e^{\frac{-t}{5}}\,</math> every <math>\,\pi\,</math> units, which neither are periodic.) |
Latest revision as of 21:01, 4 September 2008
Periodic Function: Square Wave
Given the following square wave $ \,x(t)\, $:
The function is periodic since there is a value $ \,T\, $ such that $ \,x(t+T)=x(t)\, $. In this example, the fundamental period is $ \,2\pi\, $, which one possible value for $ \,T\, $.
Non-Periodic Function: Decaying Square Wave
Given the following decaying square wave $ \,y(t)=x(t)e^{\frac{-t}{5}}\, $ ($ x(t) $ is the square wave defined in the previous section):
By inspection, this function is non-periodic, as there is no $ \,T\, $ such that $ \,y(t+T)=y(t)\, $. (The function is simply alternating between $ \,e^{\frac{-t}{5}}\, $ and $ \,-e^{\frac{-t}{5}}\, $ every $ \,\pi\, $ units, which neither are periodic.)
