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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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Presentation on theme: "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."— Presentation transcript:

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

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

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

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

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

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

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

8 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

9 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

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

11 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

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

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

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


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