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**Unformatted text preview: **(aka transfer function ) 8 9 Poles and Zeros Poles = values of z that make H(z) infinite Frequencies at which the filter blows up (gain = infinity) Zeros = values of z that make H(z) zero Frequencies which the filter eliminates (gain = 0) Note 1 : ROC H cannot contain any poles By definition, the ROC is the range of z for which the z transform is finite Note 2 : A pole-zero plot is a plot of the z plane with Symbol x is used for poles Symbol o is used for zeros 10 Stability and Causality Given H(z) with ROC = ROC H we can determine system causality and stability from ROC H Causality : Recall that the ROC of a causal signal is the region outside of the outermost pole Thus, system is casual ROC H is the region outside of the outermost pole Stability and Causality Stability : System is stable ROC H contains the unit circle. 11...

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