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Inverse Discrete Fourier Series

The questions below are due on Tuesday March 09, 2021; 10:45:00 PM.
 
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Note that this exercise is intended to be solved by hand, without the use of computation.

Determine the DT signals with the following Fourier series coefficients. Assume that the signals are periodic in N=8.

1) Part 1

What signal x_1[n] has Fourier series coefficients given by X_1[k]? Enter one period as a Python list containing [x_1[0], x_1[1], x_1[2], \ldots, x_1[7]].

One period of x_1[n] =~

2) Part 2

What signal x_2[n] has Fourier series coefficients given by X_2[k]? Enter a closed form expression for x_2[n] in terms of n and other common math constants/functions (e, j, sin, cos, etc.).

x_2[n] =~