I am working on FxLMS Algorithm for noise cancellation what changes i have to do in my code so it work properly

clc;

clear;

M = 16;

mu = 0.001;

f = 1000;

t = 0.01:0.001:0.5;

b = 1:200;

correct = sin(2*pi*t*f);

len = length(correct);

rng(0);

intrupt = 0.002 *randn(len);

x = correct + intrupt;

xref = x;

primary = [0.8 0.6 -0.2 -0.5 -0.1 0.4 -0.05];

y_d = filter(primary,1,x);

secondary = [0.9 0.6 0.1 -0.4 -0.1 0.2 0.1 0.01 0.001];

w = zeros(1,M);

xn = zeros(1,M);

e = zeros(1,M);

xhx =zeros(1,M);

for j = 1:len

xn = [xref(j) xn(1:end-1)];%secondary path adaptive filter

y_Out = sum(w.* xn);%conv of adaptive

y_ldsp = [y_Out secondary(1:end-1)];

y_final = sum(w.* secondary);%here w means weight of ldsp

e(j) = y_d(j) - y_final;

fil_x = [xref(j) secondary(1:end-1)];

LMS_x = [sum(fil_x.*secondary) xhx(1:end-1)];

w = w + mu*e(j)*LMS_x;

end

Answer 1

[Hitesh]

Hi Rajendra,

You are on the right track to implementing the FxLMS Algorithm for Noise Cancellation. Kindly ensure that reference signal is filtered through secondary path before the weight updates and recheck the weight updating equation in your code. Here are some potential improvements and corrections to your code:

Secondary Path Filtering:

• You need to ensure that the reference signal "xn" is filtered through the secondary path model before the weight update. This is crucial for the FxLMS algorithm.

Correct Weight Update:

• You can recheck the weight updating equation to use the filtered reference signal “xhx” instead of the raw reference signal “xref”.

Signal Initialization:

• You need to change "intrupt" and "x" vectors to column vectors for consistency.

Error Calculation:

• The error "e(j)" is now computed using the first element of the filtered output "y_final" to ensure proper alignment with the desired response "y_d(j)".

% Parameters 
M = 16; % Adaptive filter length 
mu = 0.001; % Step size 
f = 1000; % Frequency of the input signal 
t = 0.01:0.001:0.5; % Time vector 
len = length(t); 

% Generate signals 
correct = sin(2*pi*t*f); % Desired signal 
rng(0); % Seed for reproducibility 
intrupt = 0.002 * randn(len, 1); % Noise 
x = correct' + intrupt; % Noisy signal 
xref = x; % Reference signal 

% Primary and secondary path filters 
primary = [0.8 0.6 -0.2 -0.5 -0.1 0.4 -0.05]; 
y_d = filter(primary, 1, x); % Desired response 
secondary = [0.9 0.6 0.1 -0.4 -0.1 0.2 0.1 0.01 0.001]; 

% Initialize adaptive filter 
w = zeros(1, M); % Weights 
e = zeros(len, 1); % Error signal 

% Adaptive filtering 
for j = 1:len 
    % Shift and update the input vector 
    xn = [xref(j); zeros(M-1, 1)]; 

    % Output of adaptive filter 
    y_Out = w * xn;
    
    % Filter output through the secondary path 
    y_final = filter(secondary, 1, y_Out); 
    
    % Error calculation 
    e(j) = y_d(j) - y_final(1); 

    % Filter the reference signal through the secondary path 
    xhx = filter(secondary, 1, xn); 

    % Update weights using filtered reference signal 
    w = w + mu * e(j) * xhx'; 
end 

% Plot results 
figure; 
subplot(2, 1, 1); 
plot(t, correct); 
title('Original Signal'); 
xlabel('Time (s)'); 
ylabel('Amplitude'); 

subplot(2, 1, 2); 
plot(t, e); 
title('Error Signal'); 
xlabel('Time (s)'); 
ylabel('Amplitude'); 

For more information on "Active Noise Control Using a Filtered-X LMS FIR Adaptive Filter", refer to the below MATLAB documentation:

https://www.mathworks.com/help/audio/ug/active-noise-control-using-a-filtered-x-lms-fir-adaptive-filter.html