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\pi t/3 \,+ \,\pi/2)

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

Depending on the values of \Delta 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\hskip2em

t = \frac{1}{4}n - 3/4\hskip2em

t = \frac{3}{2}n\hskip2em

t = \frac{3}{2}n - 3/4\hskip2em

t = 0.1n\hskip2em

t = 0.2n\hskip2em

t = 0.3n\hskip2em

t = 1.4n\hskip2em

t = 1.6n\hskip2em

t = 2.9n\hskip2em

t = 1.2n\hskip2em