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Lecture 3B Questions

The questions below are due on Thursday March 04, 2021; 08:00:00 AM.
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Consider the following CT signal:

x(t) = 6\cos(42\pi t) + 4\cos(18\pi t - 0.5\pi)

What is the fundamental period of x(\cdot)?

Now imagine that this signal is sampled with a sampling rate of f_s = 60Hz to obtain a discrete-time signal x[n], which is periodic.

What is the fundamental period of x[\cdot]?

Finally, imagine finding the DTFS coefficients X[k] by analyzing x[n].

In this analysis, which values of k in the range 0\leq k < N are associated with nonzero X[k]? Enter your answer as a Python list of integers below: