Consider a quadratic function f(t) with coordinates of (3, 5), (2,4), and (4,4) such that a periodic signal (with To=6 seconds can be created as follows where u(t is the Heaviside unit step function as discussed in class p(t):= f(t-n6.{u(t-n6-u[t-6n+1]} f(t) p(t) with period of 6 seconds 10 10 2 3 4 Hint: Be sure to pay careful attention and advantage to any symmetry observed! (a) Do you observe any symmetry of p(t)? If so, how does this impact its Fourier Analysis? (b) Utilizing Fourier synthesis, express by hand a sinusoidal expression for p(t) by determining the ao, an and b. coefficients. Hint: Recall that you may need to use tabular integration or integration by parts! (c) What are the pros and cons of how you would represent this signal either with the p(t) expression above or the result of a synthesized Fourier analysis? In other words.what benefits does each signal version representation provide ? Which representation has more useful applications to the real world and WHY!