1. Find the impulse response h [n] for each of the causal LTI discrete-time systems satisfying the following difference equations and indicate whether each system is a FIR or an IIR system. (a) y[n] =x[n]- 2x[n- 2] + x[n-3] (c) y[n]y[n-2] = 2x[n]-x[n-2]

4. a) Find the complete solution for the difference equation y[n] – 0.9y[n-1] = x[n] with the input x[R]= (-1/4)"u[n] and initial condition y[-1]= 1. b) An LTI system has an impulse response h[n] and input x[n] displayed in Figure 2 below. (b.i) Apply the method of convolution by superposition to find and sketch the convolution output y[n] of the system. (b.ii) Determine and sketch the step response of this LTI system.

Consider an input x[n] and a unit impulse response h[n] given by x[n] = (½)n-2 u[n- 2], h[n] = u[n-2]Determine and plot the output y[n] = x[n] * h[n]( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).