The system function of a linear time-invariant system is given by

It is known that the system is not stable and that the impulse response is two sided.

(a) Determine the impulse response h[n] of the system.

(b) The impulse response found in Part (a) can be expressed as the sum of a causal impulse response h₁[n] and an anti causal impulse response h₂[n]. Determine the corresponding system functions H₁(z) and H₂(z).

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21 H(z) = (1 – {z-1) (1 – 2z-!)(1 – 4z-')