\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?

Signal Processing(Electronics and Communication Engineering)

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