Consider a second-order constant coefficient linear difference equation given by 1.8 y[n]+[n 1] +0.81y[n 2]...

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Consider a second-order constant coefficient linear difference equation given by 1.8 y[n]+[n 1] +0.81y[n − 2] = −2(x[n] — x[n − 2]). - - - Further, let x[n] = (3+ sin(πn/3) +0.75 cos(n)) u[n], y[-1] = 2, and y[-2] = 1. (a) By hand, recursively determine the first five terms of the zero-input response Uzir [n]. (b) By hand, recursively determine the first five terms of the zero-state response yzsr[n]. (c) By hand, recursively determine the first five terms of the total response y[n]. (d) Use MATLAB to recursively solve and then plot the first 50 terms of the zero-input, zero-state, and total responses. (e) Analytically determine the zero-input response Yzir[n]. Check this answer using the recursively computed values. Consider a second-order constant coefficient linear difference equation given by 1.8 y[n]+[n 1] +0.81y[n − 2] = −2(x[n] — x[n − 2]). - - - Further, let x[n] = (3+ sin(πn/3) +0.75 cos(n)) u[n], y[-1] = 2, and y[-2] = 1. (a) By hand, recursively determine the first five terms of the zero-input response Uzir [n]. (b) By hand, recursively determine the first five terms of the zero-state response yzsr[n]. (c) By hand, recursively determine the first five terms of the total response y[n]. (d) Use MATLAB to recursively solve and then plot the first 50 terms of the zero-input, zero-state, and total responses. (e) Analytically determine the zero-input response Yzir[n]. Check this answer using the recursively computed values.