Periodic CT Signal
In HW1, Kathleen Schremser posted the following periodic CT signal:
$ x(t)\;=\;sin(\frac{3}{4}t) $
Sampling the signal at a frequency that is an integer multiple of the frequency of the signal will result in a periodic DT signal. Sampling the signal at a frequency that is not an integer multiple of the frquency of the signal will result in a non-periodic DT signal.
$ 2\pi f=\frac{3}{4} $
$ f=\frac{3}{8\pi} $
Periodic DT Signal
Sampling the signal at a frequency $ f=\frac{3}{2\pi} $ (four times the original frequency) yields a new frequency for the periodic DT signal $ f_{DT}=\frac{1}{4} $, resulting in $ x(t)=sin(\frac{1}{2}\pi t) $, which is clearly periodic (the repeating pattern: 0,1,0,-1,0,1,0).
