(a) The difference equation
y[n] – y[n – 1] + 0.5y[n – 2] = x[n]
models an LTI system. Find the system transfer function.
(b) Find the unit step response for the system of Part (a).
(c) Use MATLAB to check the partial-fraction expansion in Part (b).
(d) From Part (b), give the values of y[0], y[1], and y[2].
(e) Verify the results of Part (d) by solving the difference equation iteratively.
(f) Verify the results in Part (e) by calculating the system’s unit-step response using MATLAB.
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