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 (2 π t / 3 + π / 2)

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

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 = \frac{1}{4} n

t = \frac{1}{4} n - 3 / 4

t = \frac{3}{2} n

t = \frac{3}{2} n - 3 / 4

t = 0.1 n

t = 0.2 n

t = 0.3 n

t = 1.4 n

t = 1.6 n

t = 2.9 n

t = 1.2 n