Inverse Fourier Series

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

The following plot shows the Fourier series coefficients a_k for a discrete-time signal x_a[n] that is periodic in n with period N=16. Determine which of the functions shown at the bottom of this page (A through H) represents the real part of x_a[n] and which represents the imaginary part of x_a[n].

Part b. The following plot shows the Fourier series coefficients b_k for a discrete-time signal x_b[n] that is periodic in n with period N=16. Determine which of the functions shown at the bottom of this page (A through H) represents the real part of x_b[n] and which represents the imaginary part of x_b[n].

Part c. The following plot shows the Fourier series coefficients c_k for a discrete-time signal x_c[n] that is periodic in n with period N=16. Determine which of the functions shown at the bottom of this page (A through H) represents the real part of x_c[n] and which represents the imaginary part of x_c[n].

Part d. The following plot shows the Fourier series coefficients d_k for a discrete-time signal x_d[n] that is periodic in n with period N=16. Determine which of the functions shown at the bottom of this page (A through H) represents the real part of x_d[n] and which represents the imaginary part of x_d[n].

Functions A through H:

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