Sampling 2

The questions below are due on Thursday February 20, 2025; 02:00:00 PM.

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Given the continuous signal

x(t) = \pi \cos(14\pi t \,+ \,1)

we can create a discrete signal x[n] by making the relation t = n/f_s, where f_s is the sampling rate (samples per second).

Part A

In each of the following problems, find a sampling rate f_s that causes x[n] to have the given fundamental period.

Fundamental Period = 2 and f_s > 5

f_s =~

Fundamental Period = 2 and 1 < f_s < 5

f_s =~

Fundamental Period = 4 and f_s > 2

f_s =~

Fundamental Period = 7 and f_s > 25

f_s =~

Fundamental Period = 7 and 5 < f_s < 25

f_s =~

Part B

Find a sampling rate f_s that causes x[n] to be equal to \pi \cos(14\pi n/14 \,+ \,1),
where 1 < f_s < 5.

f_s =~

Find a sampling rate f_s that causes x[n] to be equal to \pi \cos(14\pi n/28 \,+ \,1),
where 1 < f_s < 10.

f_s =~

Find a sampling rate f_s that causes x[n] to be equal to \pi \cos(14\pi n/49 \,+ \,1),
where 1 < f_s < 10.

f_s =~