Question A - Periodic Signals Revisited
I chose to use the CT (continuous time)periodic signal: y(t) = cos(t). The signal can be expressed as both periodic and non-periodic in DT (discrete time).
Discrete Time, Non-Periodic: Cos[n] is non-periodic in discrete time whenever it isn't sampled at $ \pi $, $ 2\pi $, or $ 0.5\pi $ (or any other multiple of $ 2\pi $). In other words, if it doesn't satisfy the equation: a[n + T] = a[n] for an integer T, then it is not periodic.
Discrete Time, Periodic: Cos[n] is periodic in discrete time when it is sampled in intervals of $ 2\pi $ (such as: $ \pi $, $ 2\pi $, or $ \pi/2 $). When sampled at this rates, it satisfies the equation: a[n + T] = a[n] for an integer T.
