a) Determine the differential equation that relates the input and output of the system. b) Find the impulse response of the system. c) Find the output of the system for input x(t) = eu(t)(1-t) everything must be solved using fourier transform methods from signals and systems course P1: Find the F.T. of the following signal using the Differentiation in frequency domain property. P2: Find the value of each of the following integrals. 00 a) 1 = | sinc* (8t)dt -00 t 2015-12 b) 1 = [ -00 2+ P3: Given a LTI system with frequency response H(w) = dt jw + 4 2 6-w +5jw