Hand written solution required

2. Consider the discrete system given below [10 marks] y[n] = 2x[n] - x[n - 1] (a) Show that the system in an LTI system (3 marks) x[n] h[n] y[n] (b) Find and sketch the system impulse response h [n], in terms of 8 [n] (2 marks) (c) Find and sketch the system output y[n] using three method, (5 marks) (n, n = 0,1,2,3,4 If the input signal is x[n] = 10, otherwise Hint: You can find y[n] using following methods: 1. System differential equation y[n] = 2x[n] - x[n - 1] 2. Mathematical equation of Convolution y[n]= x[n]*h[n] (see question 1.) 3. Graphical method using shifting and linearity property of LTI systems: Write x[n] in terms of 8 [n] and 8 [n - k], find y[n] in terms of h[n], and then graphically find y [n]