Problem 11A (i) (2 pts.) In the lecture notes, you will find the Fourier series for the symmetric (even) rectangular pulse train of unit height and duty factor o. Write down both the complex and real (cosines-only) form of the series for a fundamental period To = 8. (ii) (5 pts.) Express the periodic signal s(t) (of period To = 8) shown below as a sum of three symmetric rectangular pulse trains of the same period. Using the result of (i), derive the complex Fourier series coefficients {Sx}. Also, write down the real (cosines-only) form of the series for s(t). s(t) -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 t (iii) (3 pts.) Sketch the periodic signal x(t) which has period To = 8 (i.e., same as s(t)) and complex Fourier series coefficients given by XK = 0, k = 0; 25k, k # 0. For (iv) (vi), consider the periodic signal y(t) shown below. (t) 8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 t (iv) (1 pt.) Determine the mean value (or DC offset) of y(t). (v) (4 pts.) Determine the values taken by the derivative dy(t)/dt over one period, e.g., for