An LTI system is to be designed such that when the input to the system is x[n]=(31)nu[n]+2nu[n1] the corresponding output is y[n]=5(31)nu[n]5(32)nu[n] (a) Find the system function H(z) of this system. Make the pole zero plot for H(z) plot, and clearly indicate the ROC. (b) Find the impulse response of the system. (c) Write down a difference equation for the system. (d) Is the system stable? Explain