2/17/2007 DSP Course-IUST-Spring Semester 1

Digital Signal Processing

Electrical Engineering Department

Iran University of Science & Tech.

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Digital Signal ProcessingTopic 4: The Z TRansform

1. The Z Transform

2. Inverse Z Transform

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1. The Z Transform

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Region of Convergence (ROC)

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ROC Example

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About ROCs

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Another ROC example

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ROC is necessary!

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Rational Z-transforms

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Factored rational ZTs

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Pole-zero diagram

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Z-plane surface

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Z-plane and DTFT

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ZT is Linear

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ZT of LCCDEs

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ROCs and sidedness

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ROC intersections

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ROC intersections: Case 1

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ROC intersections: Case 2

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ROC intersections: Case 3

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ROC intersections: Case 4

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ROC intersections

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Some common Z transforms

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Z Transform properties

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Z Transform properties

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ZT Example

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Another ZT example

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2. Inverse Z Transform (IZT)

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IZT #1: Generalize IDTFT

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IZT #2: Long division

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IZT #2: Long division

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IZT #2: Long division

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IZT#3: Partial Fractions

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Partial Fractions

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Partial Fractions

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Partial Fractions Example

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Partial Fractions Example