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Lecture 22 Frequency Response Hung-yi Lee

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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

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

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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)

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

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Example 11.1 Network Function: Frequency Response:

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Example 11.1 Based on Superposition:

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Example 11.1 InputOutput

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

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

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

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Example 11.2 Phase shift network: Waveform distortion

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Another Example for Phase Shift Network

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Computing Frequency Response by Poles and Zeros

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

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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

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

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Frequency Response - Phase Shift

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Example 11.3

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Homework 11.2, 11.4

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Application: Hearing Reference: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/hearcon.html

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

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

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

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Phase and Sound Pass a Phase shift network

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Structure of Ear

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

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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

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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

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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)

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Thank you!

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Answer 11.2: 11.4:

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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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Chapter 14 Frequency Response

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