The above is a question and its solution. Can someone explain how to sketch the

Question

The above is a question and its solution. Can someone explain how to sketch the magnitude response (part b)?

I hope that I get a detailed explaination.

Thanks.

Consider a DT, causal, LTI filter with transfer function H(z), whose zero and pole locations are given by: j6R/14 j81m/14 j11/2 zero locations pole locations z 0.95, z 0.95, z 0.95 ein /6, z 0.95 e 6, z 0.95 ei5m/6 z 0.95 e-15m/6 (a) (8 pts) Plot the pole-zero diagram in the z-plane and provide the ROC of H (z). (b) (12 pts) Sketch the magnitude response IH(eju)l directly from the pole-zero plot.

Explanation / Answer

Part b can be solved by first finding the transfer function

H (z) by using the poles and zeroes location.

After that put z=e^jw we get H(e^jw)

Than we can find the magnitude of H ( e^jw) than plot can be find by finding the value of mod H(e^jw) at each angle points between the angle value corresponds to poles and zeroes.

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