Consider an LTI system with the following transfer function: -1 1-z H(z) = 1-0.5z- a) Determine the difference equation to describe the relationship between the input x[n] and output y[n] for this system. b) Determine the unit-pulse response of this system (y[n] = 0 for n < 0). c) Graph the unit-pulse response obtained in part b). d) Determine the frequency response of this system by replacing z with e e) Calculate the power gain of this filter as a function of oo and plot them using Matlab. f) What are the signal processing features of the system?