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=Periodicity= | =Periodicity= | ||
| − | The period of a periodic CT | + | The period of a periodic CT signal of the form <math>e^{j(\omega_0t+\phi)}</math> or <math>cos(\omega_0t+\phi)</math> is easy to find. This is due to the fact that every different value for the fundamental frequency <math>\omega_0</math> corresponds to a unique signal with period <math>T=\frac{2\pi}{\omega_0}</math>. |
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| + | Finding the period of a DT signal becomes more complicated. This is due to the fact that different values of <math>\omega_0</math> can in fact lead to identical equations. As an example I will show how to find the period of a DT complex exponential of the form <math>e^{j(\omega_0n+\phi)}</math> using the definition of period: a signal <math>x(n)</math> is periodic with period <math>N</math> if <math>x(n)=x(n+N)</math>. | ||
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| + | We start by applying the definition | ||
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| + | <math>e^{j(\omega_0(n+N)}</math> | ||
--[[User:Asiembid|Adam Siembida (asiembid)]] 10:09, 22 July 2009 (UTC) | --[[User:Asiembid|Adam Siembida (asiembid)]] 10:09, 22 July 2009 (UTC) | ||
Revision as of 06:17, 22 July 2009
Periodicity
The period of a periodic CT signal of the form $ e^{j(\omega_0t+\phi)} $ or $ cos(\omega_0t+\phi) $ is easy to find. This is due to the fact that every different value for the fundamental frequency $ \omega_0 $ corresponds to a unique signal with period $ T=\frac{2\pi}{\omega_0} $.
Finding the period of a DT signal becomes more complicated. This is due to the fact that different values of $ \omega_0 $ can in fact lead to identical equations. As an example I will show how to find the period of a DT complex exponential of the form $ e^{j(\omega_0n+\phi)} $ using the definition of period: a signal $ x(n) $ is periodic with period $ N $ if $ x(n)=x(n+N) $.
We start by applying the definition
$ e^{j(\omega_0(n+N)} $
--Adam Siembida (asiembid) 10:09, 22 July 2009 (UTC)
