Download
adaptive filters and active noise cancelation n.
Skip this Video
Loading SlideShow in 5 Seconds..
Adaptive Filters and Active Noise Cancelation PowerPoint Presentation
Download Presentation
Adaptive Filters and Active Noise Cancelation

Adaptive Filters and Active Noise Cancelation

266 Vues Download Presentation
Télécharger la présentation

Adaptive Filters and Active Noise Cancelation

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Adaptive Filters and Active Noise Cancelation Instructor: Jason D. Bakos

  2. Signals • Represented as a mapping between time and magnitude Dt freq=1/Dt • Sample at regular intervals .5Dt sample rate=2/Dt

  3. Signals • Sampling allows a signal to be represented as a discrete function over non-negative integers: • s(n) • vector form [0.243 1.231 0.445 3.122] aliasing adding harmonics of the sampling frequency to a sampled signal makes it appear the same

  4. The FIR Filter • Finite Impulse Response • Set of coefficients that change a signal through convolution • M-1 is the order (memory) of the filter • Example • b = [.2 .1 .5] • x = [1 5 2 4 3] • y= [.2 1.1 1.4 3.5 2.0] • Zero-pad the right side of the signal value and we do convolution • Example: (2x2 + 4x + 3) * (4x2 + 3x + 2)

  5. The FIR Filter • Filter the unit impulse reponse [1 0 0 0 …] • Result is the coefficients • Assume: • bn = 1/M for all n • Averaging filter M=8 M=16 M=24

  6. Averaging Filter on Sinusoids M=8 M=16 M=24

  7. x(5) x(4) x(3) x(2) x(1) x(4) x(3) x(2) x(1) x(2) x(1) x(3) x(2) x(1) x(6) x(5) x(4) x(3) x(2) reg reg reg reg reg b1 b2 b3 b4 b5 18 18 X X X X X 36 48 48 out + + + + DSP48 FIR Implementation • Single-cycle (parallel) implementation: x(1)

  8. = 0 reg FIR Implementation • Multi-cycle (and software) implementation: 0 to M counter rst x addressable FIFO out X + coefficients

  9. LMS Adaptive Filtering GOAL: Set the coefficients of F(x) to minimize e(x) d(n) x(n) S + - x(n) y(n) GOAL: Set the coefficients to minimize e(n) FIR e(n) LMS m can be fixed or normalized:

  10. MATLAB Example of LMS ANC • Load some speech and generate noise % load the signal signal = load('RFrost.txt'); % play it myplayer = audioplayer(signal,10000); playblocking(myplayer); % create noise % % white noise %gain = .5; %noise = gain * randn(size(signal,1),1); % % sinusoid spacing F0 = 60; A = [0.01 0.01 0.02 0.2 0.3 0.4 0.3 0.2 0.1 0.07 0.02 0.01]; noise = zeros(length(signal),1); for k = 1:length(A) noise = noise + (A(k)*sin(2*pi*F0*k/10000*(1:length(signal))+rand(1)))'; end % create the "sound" sound = signal + noise; % play the sound myplayer = audioplayer(sound,10000); playblocking(myplayer);

  11. MATLAB Example of LMS ANC • Initialize the noise filter % set the filter parameters and initialize the filter mu = .2; taps = 100; coef = zeros(1,taps); % pad the noise noise = [zeros(taps-1,1);noise]; error_out = []; out_signal = []; • Train the noise filter i = taps; while i <= size(noise,1) % compute filter output out = fliplr(coef)*noise(i-taps+1:i,1); out_signal = [out_signal;out]; % compute the error and record it error = sound(i-taps+1,1) - out; error_out = [error_out;error]; % update the step size and coefficients with nLMS step_size = mu / (noise(i-taps+1:i,1)' * noise(i-taps+1:i,1)); %step_size = mu; coef = coef + step_size * fliplr(noise(i-taps+1:i,1)') * error; i = i + 1; end

  12. MATLAB Example of LMS ANC • Play and plot % play and plot the errror myplayer = audioplayer(error_out,10000); playblocking(myplayer); n=1:length(signal); plot(n,sound',n,out_signal',n,error_out'); legend('signal + error','anti-noise','result');

  13. Filtered-X LMS ANC x(n) d(n) S + - x(n) y’(n) y(n) actual secondary path filter FIR est. secondary path filter e(n) x’(n) LMS

  14. MATLAB Example of Filtered-X ANC • Create the secondary path response % create the secondary path response % delay is 7 samples delayS = 10; N = 100; % order=9, 200 Hz to 2500 Hz, atten. in stop bands=20 [b,a] = cheby2(9,20,[200 2500]/5000); % extract impulse response impulse = [zeros(1,delayS) log(0.99*rand(1,N-delayS)+0.01) .* sign(randn(1,N-delayS)) .* exp(-0.01*(1:N-delayS))]; H = filter(b,a,impulse); H = H/norm(H); • Listen to the secondary path response % play the sound myplayer = audioplayer(sound,10000); playblocking(myplayer); % create and play the sound received from the error mic received_sound = filter(H,1,sound); myplayer = audioplayer(received_sound,10000); playblocking(myplayer);

  15. MATLAB Example of Filtered-X ANC • “Learn” the secondary path response % learn the secondary path filter and filter the received noise white_noise = randn(1,30000); received_noise = filter(H,1,white_noise); h=adaptfilt.nlms(250,.1,1,.1); [yS,eS] = filter(h,white_noise,received_noise); • Filter X! ref. error % filter reference with 'our' filter % this is what implements filtered-x noise_filtered=filter(h.coefficients,1,noise); • Initialize the noise filter % set the filter parameters and initialize the filter mu = .0001; taps = 350; coef = zeros(1,taps); % pad the noise noise = [zeros(taps-1,1);noise]; noise_filtered = [zeros(taps-1,1);noise_filtered]; error_out = []; error_filtered_out = []; out_signal = zeros(length(H)-1,1);

  16. MATLAB Example of Filtered-X ANC • Train the noise filter i = taps; j = length(H); while i <= size(noise,1) % compute filter output out = fliplr(coef)*noise(i-taps+1:i,1); out_signal = [out_signal;out]; % filter the filter output out_filtered = fliplr(H) * out_signal(j-length(H)+1:j,1); j = j + 1; % compute the error and record it error = sound(i-taps+1,1) - out_filtered; error_out = [error_out;error]; % update the step size and coefficients with nLMS %step_size = mu / (noise_filtered(i-taps+1:i,1)' * noise_filtered(i-taps+1:i,1)); step_size = mu; coef = coef + step_size * fliplr(noise_filtered(i-taps+1:i,1)') * error; i = i + 1; % debug if mod(i,2000) == 0 coef end end

  17. MATLAB Example of Filtered-X ANC