(a) Using Fourier transform, find the output y(t) for the input x(t) = etu(t) for the continuous-time LTI system described by: dy(t) + 2 y(t) = x(t) plZ dt (b) A causal discrete-time LTI system,...

Extracted text: (a) Using Fourier transform, find the output y(t) for the input x(t) = etu(t) for the continuous-time LTI system described by: dy(t) + 2 y(t) = x(t) plZ dt (b) A causal discrete-time LTI system, having input x[n] and output y[n], has impulse response h[n] given by: SOve A[n] = [2(})" - (})"]«[n]) Where u[n] represents the unit step function. Using the Discrete-time Fourier Transform, (i) determine the frequency response of the system. (ii) express the dynamics of the system in terms of a differential equation.