Problem 1: Approximating a continuous-time system A continuous-time filter has the transfer function G(s) = 8+1 (s+3)(8+12) a) Use each of the following methods to find the transfer function H(2) of a discrete-time system with sampling period T = 0.1 that approximates the continuous-time system G(s). • impulse invariance • step invariance ⚫ bilinear transform b) Plot the impulse response of both G(s) and the approximation using impulse invariance on the same axis. c) Plot the step response of both G(s) and the approximation using step invariance on the same axis. d) Plot the frequency response of both G(s) and the approximation using the bilinear transform on the same axis.