Problem 6. For a system with a given impulse response h[n]=0.3 \delta[n]+0.1666(0.2)^{n} u[n]+0.5333(0.5)^{n} u[n] a. Find H(z). (Hint: you can easily forward-transform h[n] using the look-up table) b. Determine the

inverse system Hi(z). Using a PFE, determine the impulse response for the inverse system hi[n]. d. Using MATLAB, plot h[n], h;[n], and h[n] *hi[n] for n =[0,20] to verify that hi[n] is indeed an inverse system to h[n].