Problem #1. a) (Fourier Synthesis) Create a partial Fourier series sum in Excel for the n interval [0,8] and t time interval [-, x), using the following Fourier series coefficients obtained by the equations in the textbook. Break the time interval into 200 intervals, estimate g(() with a partial Fourier series. I. Plot the Fourier synthesis (sum) in Excel using lab report protocols. Make sure to submit the excel file. II. The final plot of the synthesis should be inserted here as a picture. A A. A- 3.2890 4 -1 0.4444 -0.25 0.16 -0.11111 0.08163 -0.0625 B B. B. BA B- -1 0.66667 -0.5 0.4 -0.33333 0.285714286 -0.25 b) (Fourier Analysis) Show that the coefficients were obtained from the Fourier series equations for a periodic function, f(t) = t-, - Six I. Present all step for calculating Fourier coefficients (As, A, and B.). you may calculate those integrals via using mathematic sources or any online integral solution sources. II. Plot the f(t) = t-to, -* $1 in the same Excel file as Problem#1.a and compare it with its synthesis plot for the first 8 sentences of Fourier (as you plot it in 1.a). The final comparing plot of the synthesis (from 1.a) and f(t) = t-: should be inserted here as a picture. c) using an online function plotter (https://www.desmos.com/calculator), I. draw the Take a screen shot of this function and insert it here. The picture should be your full screen including the function and the plot. Zoom the plot to limit the t axis to about$ 10 tt