Alternative Representations
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Part a. Let c_k and d_k represent the trigonometric Fourier series coefficients for a periodic function f_1(t) of continuous time t with period T:
Enter expressions for c_0', c_1', d_1', c_2', d_2', c_3', and d_3' in a tabular form, as illustrated below. Your expressions may contain any combination of the original (unprimed) coefficients (c_0, c_1, c_2, ... and d_0, d_1, d_2, ...) but must not include f_1(t) or f_2(t) or any integrals or infinite sums.
Notice that d_0' is not defined, and it's box is x'd out of the table.
Briefly explain.
Part b. Let a_k represent the complex exponential Fourier series coefficients for a periodic function f_3(t) of continuous time t with period T:
as functions of the original (unprimed) coefficients (a_k).
Enter expressions for a_{-2}', a_{-1}', a_0', a_1', and a_2' in the table below. Your expressions may contain any combination of the original (unprimed) coefficients a_k but must not include f_3(t) or f_4(t) or any integrals or infinite sums.
Briefly explain.