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Zhiyun Kuang © May, 2004 Adaptive Notch Filter Application on modifying signal without changing frequency domain.

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Zhiyun Kuang © May, 2004 Copyright of Sound bank $10,000 spent to record one piano sound bank. Easy to make illegal copy. Want to make characteristic on the signal without corrupting it.

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Zhiyun Kuang © May, 2004 Sound properties Sound: A x Sin(2πω+Ө) A => Magnitude => Loudness ω => Frequency => Pitch, Location Ө => Phase => reverb, echo, loudness

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Zhiyun Kuang © May, 2004 Time domain vs Frequency domain

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Zhiyun Kuang © May, 2004

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Two problems: 1.Avoid canceling other frequency 2.Track original signal

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Zhiyun Kuang © May, 2004 Least Mean Square algorithm

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Zhiyun Kuang © May, 2004 Matlab Code x1 = C*cos(2*pi*w0*t); x2 = C*sin(2*pi*w0*t); x3 = C*cos(2*pi*w0*t+theta); x4 = C*sin(2*pi*w0*t+theta); for i = L:length(T) temp_x1 = x1(i:-1:i-L+1); temp_x2 = x2(i:-1:i-L+1); temp_x3 = x3(i:-1:i-L+1); temp_x4 = x4(i:-1:i-L+1); yk1 = sum(w1.*temp_x1); yk2 = sum(w2.*temp_x2); yk3 = sum(w1.*temp_x3); yk4 = sum(w2.*temp_x4); y(i) = yk1+yk2; yref(i) = (yk3+yk4); e = d(i)-y(i); for j=(1:L) w1(j)=w1(j)+2*u*e*temp_x1(j); w2(j)=w2(j)+2*u*e*temp_x2(j); end

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Zhiyun Kuang © May, 2004

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Conclusion Can use notch filter to filter certain frequency, but hard to improve accuracy and track the represent signal. Adaptive notch filter can easily control the width of the filter and track the represent signal. Using the relationship of the C, μ, ө, can change a signal to have some characteristic, without changing its frequency domain.

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