1. A discrete-time system with input x[n] and output y[n] is described by the difference equation (a) y[n] = x[n] + 2x[n 1] + x[n 2] i. Classify the system as A. Linear or non-linear B. Causal or non-causal C. Stable or not stable D. FIR or IIR ii. Find its impulse response. iii. Use two methods to find the output y[n] if x[n] = {..0, 0, 1, 2, 3, 10, 8, 6, 0, 0...}. The two methods are a) Using the difference equation, b) Using convolution. iv. (MATLAB)Find the output y[n] when x[n] = cos(won) where wo = {0, 1, 2, 3, 4}/4 radians per sample. Use 5 subplots to plot input and output on the same set of axes. Include label, title and legends in the figures. v. (MATLAB) Use a separate figure to stem the (positive) ampli- tude of each one of the outputs above as a function of frequency. Comment on the result and the system's frequency selection. (b) Repeat the questions (i), (ii) and (iii) above for the systems described by y[n] = e*[n] For question (iii), just find the output y[n] using the system equation. Can you use convolution to find the output? Explain. 2. Compute the convolution y[n] = x[n] *h[n] where h[n] = {..0, 0, 0.5, 0.5, 0, 0, ...} and (a) x[n] = {..0, 0, 1, 5, 3, 7, -2, 0, 0, ...} and (b) x[n] = ej.25nu[n]. Express your answer in the form of y[n] Ae(wn+0) where all the parameters are real valued. 3. Consider the system described by the input-output equation y[n] = x[n] - x[n 1] + ay[n 1] = for the two cases of a = [0.2,2]. (a) Find the system impulse response h[n] for each value of a and sketch it, by hand, versus n. (b) Is the system FIR or IIR? Why? (c) Find the system output y[n] for x[n] = {..0, 0, 0.5, 1,5, 0, ...}. (d) (MATLAB) Find the system output y[n] for x[n] = cos(won)u[n] for frequencies wo= {0, 1,.., 15}.