Chapter 3 the z-Transform

1. Chapter 3 the z-Transform 3.1 definition 3.2 properties of ROC 3.3 the inverse z-transform 3.4 z-transform properties

2. 3.1 definition Figure 3.2

3. the condition for convergence：

4. ROC takes the poles as its boundary EXAMPLE:

5. 3.2 properties of ROC

7. 3.3 the inverse z-transform 1.inspection method 2.partial fraction expansion 3.power series expansion

8. EXAMPLE: EXAMPLE:

9. 3.4 z-transform properties

11. 7.x[n] is causal

12. EXAMPLE:

13. Relation between H(z) and frequency responce: B=[2,1,0,-1] A=[1,0,0.5,0,-1] freqz(B,A)

15. summary: 3.1 the z-transform 3.2 properties of ROC right-sides sequence: inside the circle left-sides sequence: outside the circle finite-duration sequence: the entire z-plane two-sided sequence: a ring causal sequence: including infinite stable sequence: including the unit circle 3.3 the inverse z-transform: inspection method partial fraction expansion power series expansion 3.4 z-transform properties

16. Keys and difficulties： ROC; the convolution property; the relationship among system function, the impulse response, frequency response and difference equation; exercises: 3.37 3.38 （these can be solved without contour integral method）