Transcript Adaptive Notch Filter

Adaptive Notch Filter
Application on modifying signal without changing
frequency domain.
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.
Zhiyun Kuang © May, 2004
Sound properties
• Sound: A x Sin(2πω+Ө)
• A => Magnitude => Loudness
• ω => Frequency => Pitch, Location
• Ө => Phase => reverb, echo, loudness
Zhiyun Kuang © May, 2004
Time domain vs Frequency domain
Zhiyun Kuang © May, 2004
Zhiyun Kuang © May, 2004
Two problems:
1. Avoid canceling other frequency
2. Track original signal
Zhiyun Kuang © May, 2004
Least Mean Square algorithm
Zhiyun Kuang © May, 2004
Matlab Code
x1 = C*cos(2*pi*w0*t);
x2 = C*sin(2*pi*w0*t);
y(i) = yk1+yk2;
yref(i) = (yk3+yk4);
e = d(i)-y(i);
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);
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
end
yk1 = sum(w1.*temp_x1);
yk2 = sum(w2.*temp_x2);
yk3 = sum(w1.*temp_x3);
yk4 = sum(w2.*temp_x4);
Zhiyun Kuang © May, 2004
Zhiyun Kuang © May, 2004
Zhiyun Kuang © May, 2004
Zhiyun Kuang © May, 2004
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.
Zhiyun Kuang © May, 2004