ecen4763.notes.42

ecen4763.notes.42 - (aka transfer function 8 9 Poles and...

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1 ECEN 4763: Introduction to Digital Signal Processing Fall 2009 Lecture 42: Monday, November 30, 2009 z Transform, Part III 1. Table of transform pairs 2. Properties of the z transform 3. System analysis using the z transform
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2 z Transform, Part III 1. Table of transform pairs 2. Properties of the z transform 3. System analysis using the z transform Common z transform pairs
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3 Common z transform pairs (See Appendix C in the text for more transform pairs.) z Transform, Part III 1. Table of transform pairs 2. Properties of the z transform 3. System analysis using the z transform
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4 Properties of the z transform Properties of the z transform
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5 Properties of the z transform z Transform, Part III 1. Table of transform pairs 2. Properties of the z transform 3. System analysis using the z transform – System response (transfer function) – System properties
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6 System Response System Response
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7 System Response System response is the z transform of h(n)
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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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ecen4763.notes.42 - (aka transfer function 8 9 Poles and...

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