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Please answer the question below for all parts. Please show all work and write clearly. Thanks....

Please answer the question below for all parts. Please show all work and write clearly. Thanks. (You may use Excel or Matlab to make the calculations easier, but must show work and code).

A 1 kHz sine wave is sampled at frequency of 5 kHz.

(a) What is the Nyquist frequency of the sampling system in this case? Show your work.

(b) What is the Nyquist rate of the signal? Show your work.

(c) Is the signal properly sampled; that is, will there be aliases in the digitally recorded signal? Explain.

(d) What if the original analog signal included both even and odd harmonics of its primary frequency; that is, 2, 3, 5 kHz, etc. What would be the highest harmonic that will be faithfully represented in the discrete-time version of the analog signal?

(e) Following on with the previous step, what is the lowest harmonic that will be aliased and what would be resulting alias frequency?

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