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A linear time invariant system has an impulse response given by ℎ[?] = 2(−0.5) ? ?[?]...

A linear time invariant system has an impulse response given by ℎ[?] = 2(−0.5) ? ?[?] − 3(0.5) 2? ?[?] where u[n] is the unit step function.

a) Find the z-domain transfer function ?(?).

b) Draw pole-zero plot of the system and indicate the region of convergence.

c) Is the system stable? Explain.

d) Is the system causal? Explain.

e) Find the unit step response ?[?] of the system, that is, the response to the unit step input.

f) Provide a linear constant coefficient difference equation representation of the system.

g) Sketch a block diagram representation of the system using multipliers, adders, and unit delays.

h) Compute the frequency response H(e^jw) and plot its magnitude for 0<=w<=pi . Is this system a low-pass filter, a high-pass filter, or a bandpass filter? Explain.

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