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Lecture 22 Frequency Response Hung-yi Lee Filter Outline (Chapter 11) Amplitude Ratio Phase Shift Highpass Filter Frequency Response Bode Plot Draw frequency.

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Presentation on theme: "Lecture 22 Frequency Response Hung-yi Lee Filter Outline (Chapter 11) Amplitude Ratio Phase Shift Highpass Filter Frequency Response Bode Plot Draw frequency."— Presentation transcript:

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2 Lecture 22 Frequency Response Hung-yi Lee

3 Filter Outline (Chapter 11) Amplitude Ratio Phase Shift Highpass Filter Frequency Response Bode Plot Draw frequency response Ch 11.4 Ch 11.1 Ch 11.2 Lowpass Filter Notch Filter Bandpss Filter

4 Review Network Function Output depends on input and complex frequency s.

5 Frequency Response Only focus on the change of frequency In this lecture, we only focus on s=jω. H(jω) is the frequency response. That is, only consider H(jω)

6 Frequency Response H(jω) is a complex number, so frequency response is usually represented by two curves Magnitude Ratio Phase Shift

7 Example 11.1 Network Function: Frequency Response:

8 Example 11.1 Based on Superposition:

9 Example 11.1 InputOutput

10 Example 11.2 Assume C=1/aR Find Network Function a=1/RC

11 Example 11.2 Set s=jω The amplitude ratio is constant.

12 Example 11.2 Magnitude Ratio Phase Shift Distance of jω to a Distance of jω to -a

13 Example 11.2 Phase shift network: Waveform distortion

14 Another Example for Phase Shift Network

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16 Computing Frequency Response by Poles and Zeros

17 Frequency Response K: gain factor p 1, p 2, …: poles z 1, z 2, …: zeros

18 Frequency Response - Magnitude Ratio Distance of jω to z 1 Distance of jω to p 1 Distance of jω to p 2 Distance of jω to z 2

19 Frequency Response - Magnitude Ratio Gain factor is K Magnitude ratio at ω =| Gain factor| all distance to zeros all distance to poles X

20 Frequency Response - Phase Shift

21 Example 11.3

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24 Homework 11.2, 11.4

25 Application: Hearing Reference:

26 Range of Hearing Range of Audio: 300Hz – 3.4KHz Frequency Range of hearing: 20Hz - 20KHz dB

27 Equal Loudness Contour Red Curve: Equal loudness Blue Line: Same Energy 60 phon means as loud as the 60dB 1kHz sound. phon (unit): dB

28 Hearing v.s. Age Application: 柯南 68 集 ( 黑暗中消失的麒麟之角 )

29 Phase and Sound Pass a Phase shift network

30 Structure of Ear

31 Cochlea ( 耳蝸 ) to brain Each neuron only passes a specific frequency. Pass high frequency Pass low frequency Pass 20kHz Pass 20Hz

32 Cochlea ( 耳蝸 ) to brain Neuron for ω=300 Neuron for ω=100 Neuron for ω=20 ω=300, Amplitude=10 ω=20, Amplitude=10

33 Machine Hearing Each triangle is the amplitude ratio of a filter How? Ear of machine A set of filters (filter bank) Energy of the signal of the output of the filter Send to computer How to write a program for speech recognition? a. Observe data, and write down some rules b. Simulate human brain, and let the computer learn by itself. Feature

34 Speech Signal 文藝 ? 聞腋 ? Acoustic Model Language Model Text Machine Learning Deep Neural Network (Brain) Features Speech Recognition Signal Processing ㄨㄣˊ ㄧˋ … (Filter Bank)

35 Thank you!

36 Answer 11.2: 11.4:

37 Acknowledgement 感謝 陳俞兆 (b02) 上課時指出投影片的錯誤 感謝 陳均彥 (b02) 上課時指出投影片的錯誤 感謝 林楷恩 (b02) 指出投影片方程式的錯誤


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