Inverse Discrete-Time Fourier Series

The questions below are due on Thursday February 27, 2025; 02:00:00 PM.

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

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] =~

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] =~