The exponential Fourier series coefficients of a signal x(t) are given below This implies that the Fourier series coefficients are defined as |Dn|ej∠Dn (a) Find the exponential series representing x(t). (b) In MATLAB, plot the trigonometric Fourier spectra for x(t), and include the plot here. (c) Find the trigonometric Fourier series representing x(t). (d) Show that the two series are equivalent.
![Problem 4: Fourier Series [24 points] (a) (6 points) Obtain the Fourier series of the signal x(t) given in Figure 3. Using numerical solvers (like Wolfram alpha), sketch the synthesis equation of the Fourier series and see if it gives the same sketch as in Figure 3. Figure 3: Figure for Question 4 part (a) (b) (6 points) Consider a signal g(t) = t2 over the interval (−1, 1) which repeats its self with a period T = 4. Find the trigonometric Fourier Series to represent g(t). Sketch the Fourier Series over frequency. (c)(6 points) Verify Parseval's Theorem for this case given that ∑n = 1∞1 n4 = π490 (d) (6 points) Determine the periodic signal x(t) of period T = 4 whose Fourier series coefficients are given below cn = {jn|n| < 30 otherwise](https://www.doubtrix.com/uploads/editor/0258520695NeIiMMsiju.png)
