Question
\text { Suppose that the input to a causal LTI system is } x[n]=\frac{1}{4}\left(-\frac{1}{3}\right)^{n} u[n]-3 \times 4^{n} u[-n-1] and the z-transform of the output y[n] is Y(z)=\frac{13 / 4}{\left(1-\frac{1}{2} z^{-1}\right)\left(1-z^{-1}\right)\left(1+\frac{1}{3}
z^{-1}\right)} (a) Find the z-transform of a[n] and its ROC. b) Find the transfer function H(z) and its ROC. :) Determine the ROC of Y(z). (d) Find the impulse response of the system. =) Is the system stable?
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