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==Non-Periodic== | ==Non-Periodic== | ||
| − | <math>x[n]=\cos{n}</math> is an example of a non-periodoc signal because there is not integer value for n such that <math>x[n+N]=x[n]</math>. It would be periodic if <math>N=K* | + | <math>x[n]=\cos{n}</math> is an example of a non-periodoc signal because there is not integer value for n such that <math>x[n+N]=x[n]</math>. It would be periodic if <math>N=K*2\pi</math>, but <math>\pi</math> is not an integer and therefore can not be chosen. |
Revision as of 14:09, 4 September 2008
Periodic
$ x[n]= $$ j^{n} $ is a discrete time (DT) periodic signal. It's period is 4*k, where k is an integer. However, it's fundamental period is 4.
$ j^{1}=-1 $
$ j^{2}=-j $
$ j^{3}=1 $
$ j^{4}=j $
$ j^{5}=-1 $
$ j^{6}=-j $
$ j^{7}=1 $
$ j^{8}=j $
Non-Periodic
$ x[n]=\cos{n} $ is an example of a non-periodoc signal because there is not integer value for n such that $ x[n+N]=x[n] $. It would be periodic if $ N=K*2\pi $, but $ \pi $ is not an integer and therefore can not be chosen.
