1. Signals and Systems Using MATLAB Luis F. Chaparro

2. 2 Chapter 9 - The Z-transform

3. 3 What is in this chapter? Laplace transform of sampled signals and Z- transform Two- and one-sided Z- transforms Poles and zeros and region of convergence Convolution sum and transfer function Inverse Z-transform Solution of difference and differential equations

4. 4 Laplace transform of sampled signals

5. 5 Two-sided and one-sided Z-transform

6. 6

7. 7 Poles and Zeros

8. 8

9. 9

10. 10

11. 11

12. 12 Convolution Sum and Transfer Function

13. 13

14. 14

15. 15

16. 16

17. 17

18. 18 Interconnection of discrete-time systems Cascade Negative feedback Parallel

19. 19

20. 20 One-sided Z-transform Inverse Inspection Long-division

21. 21 Partial Fraction Expansion

22. 22

23. 23 Partial Fraction Expansion with MATLAB

24. 24 Example

25. 25

26. 26 Solution of Difference Equations

27. 27

28. 28 Solution of Differential Equations

29. 29

30. 30 Inverse of Two-sided Z-transforms

31. 31 What have we accomplished? Fourier analysis of discrete-time systems Where do we go from here? Connection of Laplace and Z- transforms Solution of difference and differential equations with initial conditions Significance of poles and zeros in z-plane and poles for ROC Application of Z-transform to control Frequency representation of discrete-time systems Transfer function of recursive and non-recursive filters