1. 1 Signals and Systems Lecture 22 Aliasing

2. 2 Chapter 7 Sampling Sampling Theorem: Let be a band-limited signal with then is uniquely determined by its samples if where

3. 3 Chapter 7 Sampling §7.3 The Effect of Undersampling: Aliasing 欠采样 混叠 Let P565 7.25

4. 4 Chapter 7 Sampling 1. Consider a sinusoidal signal Fix, change Figure (a)

5. 5 Chapter 7 Sampling

6. 6 Figure (b)

7. 7 Chapter 7 Sampling Figure (c)

8. 8 Figure (d) Chapter 7 Sampling

9. 9 When aliasing occurs, 2. Consider a sinusoidal signal

10. 10 Chapter 7 Sampling

11. 11 Chapter 7 Sampling 3.

12. 12 Anti-Alias Filtering (AAF) Therefore, the first step in sampling is anti-alias filtering (AAF) –– a LPF to assure that Chapter 7 Sampling

13. 13 The effect of AAF The AAF low- pass filter will rid of the information in x(t) beyond, but will avoid the much more serious aliasing problem. Chapter 7 Sampling

14. 14 Chapter 7 Sampling Excise 7.8 (P558)

15. 15 Chapter 7 Sampling Excise 7.9 (P558)

16. 16 Chapter 7 Sampling Excise 7.10 (P558) a. x(t) is not a periodic signal. b. |ω|< ω 0 c.

17. 17 Chapter 7 Sampling 4. Strobe Effect （频闪效应） Figure 7.18 The speed of rotation of the disc is perceived correctly. The rotation appears to be at a lower frequency than is actually the case. Furthermore, because of phase reversal, the disc will appear to be rotating in the wrong direction. Rotating disc Strobe

18. 18 Excise 7.38(P570) Chapter 7 Sampling

19. 19 Chapter 7 Sampling

20. 20 Chapter 7 Sampling

21. 21 Chapter 7 Sampling Assume:

22. 22 Chapter 7 Sampling Consider the general case:

23. 23 Chapter 7 Sampling

24. 24 Summary Analysis of aliasing phenomenon

25. 25 Readlist Signals and Systems: –7.4~7.5

26. 26 Chapter 6 Time and Frequency Characterization Homework: P564 7.26