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Consider a causal LTI system described by the difference equation: y[n] = 0.5 y[n-1] + x[n]...


Consider a causal LTI system described by the difference equation:
y[n] = 0.5 y[n-1] + x[n] – x[n-1]
(a) Determine the system function H(z) and plot a pole-zero pattern in the complex z-plane.
(b) Find the system response using partial fraction expansion when the input is x[n] = 2u[n]. Plot the result.

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