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16.362 Signal and System I The inverse z-transform Any path in the ROC to make the integral converge Example ROC |z|>1/3

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16.362 Signal and System I The inverse z-transform Example ROC 1/4 <|z|<1/3 Example ROC |z|<1/4

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16.362 Signal and System I The inverse z-transform Example ROC 0 <|z|< Example |az -1 |<1

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16.362 Signal and System I Geometric evaluation of the Fourier Transform from the pole-zero plot ROC 1 Unit circle x First order

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16.362 Signal and System I Geometric evaluation of the Fourier Transform from the pole-zero plot ROC 1 Unit circle x

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16.362 Signal and System I Geometric evaluation of the Fourier Transform from the pole-zero plot ROC 1 Unit circle x 2 nd order x

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16.362 Signal and System I Properties of z-transform (1) Linearity with ROC containing with ROC R1 with ROC R2

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16.362 Signal and System I (2) Time shifting with ROC R1 with ROC R1 with addition or deletion of poles at z=0 or infinite (3) Scaling in the z-domain with ROC |z0|R1 with ROC R1 with addition or deletion of poles at z=0 or infinite

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16.362 Signal and System I (3) Scaling in the z-domain with ROC |z0|R1 with ROC R1 with addition or deletion of poles at z=0 or infinite x x

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16.362 Signal and System I (4) Time reversal with ROC R1 with ROC 1/R1

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16.362 Signal and System I (5) Time expansion if n is a multiple of k otherwise with ROC (R) 1/k (6) Conjugation with ROC R real with ROC R

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16.362 Signal and System I (7) Convolution with ROC R1 with ROC R2 Example

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16.362 Signal and System I Differentiation in z-domain with ROC R1 Example

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16.362 Signal and System I Initial value theorem for n<0 Example, check the correctness of a z-transform

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16.362 Signal and System I Causality ROC for n < 0 causal All z -n terms, not include any z terms If and only if ROC is exterior of a circle and include.

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