Problem 1 We want to design a causal discrete-time LTI system with the property that if the input is æ[n] = (})" u[n] – }G)"-"u[n-1] | then the output is y[n] = (})" u[n]. (a) Determine the impulse response hn] of a system that satisfies the foregoing conditions. (b) Find the difference equation that characterizes this system. (c) Determine a realization of the system that requires the minimum amount of memory. (d) Determine if the system is stable.

Question 4. Consider a causal system whose input output relationship is given by yln] -yln – 1] +yln – 2] = x[n]. a) Find its system function. b) Find its impulse response. c) Repeat part b if the system is uncausal.

(A) Two LTI sub-systems with individual impulse responses h1[n] and h2[n] are given below: h1[n] = [2, 2, -10, 7, 25), -3sns1 h2[n] = [-2, 0, 0, 8, 0, 6), Osns5 1- Test the causality and stability of h1[n] only. 2- Connect the two sub-systems in parallel, then find the overall (total) impulse response. Hint: Use the convolution property to decide the process between h1[n] and h2[n].

Show your detailed soln please