Sampling

The questions below are due on Thursday February 20, 2025; 02:00:00 PM.
 
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We can create arbitrarily many discrete signals from a single continuous signal by sampling the continuous signal regularly at different intervals. For instance, given the signal

x(t)=cos(2πt/3+π/2)

we can create the discrete signal x[n] by making the relation t=Δn+s.

Depending on the values of Δ and s, the apparent period of x[n] can vary. For each of the following relations, determine the fundamental period of x[n]. If the signal becomes constant, type "None".

t=14n
t=14n3/4
t=32n
t=32n3/4
t=0.1n
t=0.2n
t=0.3n
t=1.4n
t=1.6n
t=2.9n
t=1.2n