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For an LTI system h[n], the output is given by y[n] = 2δ[n-1], given that x[n]...

For an LTI system h[n], the output is given by
y[n] = 2δ[n-1],
given that
x[n] = δ[n]-2δ[n-1]+ 2δ[n-2].
a) Find the transfer function H(z) (7 Points).
b) Find the difference equation of the overall system (8 Points).
c) Given that the system is causal find h[n] (10 Points).
d) Given that the system does not have Fourier Transform, find h[n] (10 Points).

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