1 Signals and Systems Lecture 22 Aliasing. 2 Chapter 7 Sampling Sampling Theorem: Let be a band-limited signal with then is uniquely determined by its.

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Presentation transcript:

1 Signals and Systems Lecture 22 Aliasing

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

3 Chapter 7 Sampling §7.3 The Effect of Undersampling: Aliasing 欠采样混叠 Let P

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

5 Chapter 7 Sampling

6 Figure (b)

7 Chapter 7 Sampling Figure (c)

8 Figure (d) Chapter 7 Sampling

9 When aliasing occurs, 2. Consider a sinusoidal signal

10 Chapter 7 Sampling

11 Chapter 7 Sampling 3.

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 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 Chapter 7 Sampling Excise 7.8 (P558)

15 Chapter 7 Sampling Excise 7.9 (P558)

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

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 Excise 7.38(P570) Chapter 7 Sampling

19 Chapter 7 Sampling

20 Chapter 7 Sampling

21 Chapter 7 Sampling Assume:

22 Chapter 7 Sampling Consider the general case:

23 Chapter 7 Sampling

24 Summary Analysis of aliasing phenomenon

25 Readlist Signals and Systems: –7.4~7.5

26 Chapter 6 Time and Frequency Characterization Homework: P