Zhiyun Kuang © May, 2004 Adaptive Notch Filter Application on modifying signal without changing...
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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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Zhiyun Kuang © May, 2004
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 Codex1 = 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); endend
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Zhiyun Kuang © May, 2004
![Page 10: Zhiyun Kuang © May, 2004 Adaptive Notch Filter Application on modifying signal without changing frequency domain.](https://reader036.fdocument.pub/reader036/viewer/2022070415/56649cc25503460f9498ae38/html5/thumbnails/10.jpg)
Zhiyun Kuang © May, 2004
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Zhiyun Kuang © May, 2004
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Zhiyun Kuang © May, 2004
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Zhiyun Kuang © May, 2004
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.