Periodic Signals Revisited
1. By sampling at different frequencies the function $ y=sin(x)\! $ can appear as both periodic and non-periodic in DT. For example:
$ y(x)=sin(x) \! $ in CT
$ y[n]=sin[n] \! $ with a sample rate of 1
$ y[n]=sin[n] \! $ with a sample rate of $ pi/4 \! $
The second graph has no integer value of N where y[n]=y[n+N], thus it is non-periodic.
The third graph clearly shows there is an integer value of N where y[n]=y[n+N], thus it is periodic.
