Let X(2) be a causal LTI system with its poles and zeros located in the unit circle. Further,assume that the ROC includes the unit circle. We can express this system generically as: X(z)=A \frac{\prod_{k=1}^{M_{1}}\left(1-\alpha_{k} z^{-1}\right)}{\prod_{k=1}^{N_{1}}\left(1-\gamma_{k} z^{-1}\right)} where M1 are the number of zeros and and N1 are the number of zeros. You can assumethat for complex conjugate zeros (poles) that ak = a; (7k = V;). The Cepstrum is definedas C_{x}(z)=\log X(z) Using the information above, find c[n] (i.e., the time domain sequence for C(2)). Hints • You only need to find c[n] for n > 0. It might be helpful to have your Maclaurin series look-up tables nearby.

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let x2 be a causal lti system with its poles and zeros located in the

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Let X(2) be a causal LTI system with its poles and zeros located in the unit circle. Further,assume that the ROC includes the unit circle. We can express this system generically as: X(z)=A \frac{\prod_{k=1}^{M_{1}}\left(1-\alpha_{k} z^{-1}\right)}{\prod_{k=1}^{N_{1}}\left(1-\gamma_{k} z^{-1}\right)} where M1 are the n