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)