Problem 1. The output of an LTI system is described by y[n]=y[n-1]-0.5 y[n-2]+x[n]+x[n-1] where y[n] = 0 for n < 0, i.e., the initial-conditioned response yi[n] = 0. a. Draw

a block diagram using multipliers, adders, and shifters that represents the system. b. Determine the characteristic equation. c. Determine the analytical form of the impulse response function, h[n] (hint: roots are complex). d. Plot h[n] in MATLAB for n=0,1, ..., 20. e. Is the system stable? Explain. f. Explain how you would go about calculating the total system response for an input of x[n] = u[n] (NOTE: do not perform any calculations, just set up the equation).