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Periodic CT and DT Signals
Background
When given a CT signal, DT signals can be produced by sampling the CT at certain intervals. For Example: Given the periodic signal $ 4cos(\pi t) $, The following 2 signals can be produced, one periodic and one not.
CT Periodic Signal
DT Periodic Signal
This function has a sampling frequency of 1 unit.
DT Non-Periodic Signal
If we now sample this function at $ \frac{1}{\pi} $, the equation would turn into $ 4cos[n] $ , giving
which is not periodic.
