is it possible to remove thermal noise completely from audiofile by using nlms or rls algorithm?

% below is the code I came up with after many different references but some residue thermal noise still remains and % the filtered signal sounds grainy can it be made better or this is it

function adaptive_nlms_audio_filter()

% Adaptive NLMS Audio Noise Filtering with Dynamic Parameter Adjustment

clc;

clear;

close all;

% Get audio input from the user

[audio, fs] = getAudioInput();

% Normalize the audio

audio = audio / max(abs(audio));

% Add Nyquist-Johnson noise (white Gaussian noise)

noise_power = 0.01; % Adjust noise power as needed

noise = sqrt(noise_power) * randn(size(audio)); % Generate noise

noisy_audio = audio + noise;

% Analyze the spectrum of the input audio

[freq, magnitude] = analyzeSpectrum(noisy_audio, fs);

% Adaptive NLMS Parameters

M = determineFilterOrder(freq, magnitude); % Dynamically determine filter order

mu = determineStepSize(magnitude); % Dynamically determine step size

epsilon = 1e-6; % Regularization factor

w = zeros(M, 1); % Filter coefficients

filtered_nlms = zeros(size(noisy_audio));

% Adaptive filtering using NLMS

for i = M:length(noisy_audio)

x = flip(noisy_audio(i-M+1:i)); % Input vector

e = audio(i) - w' * x; % Error signal

w = w + (mu / (epsilon + norm(x)^2)) * x * e; % Update filter coefficients

filtered_nlms(i) = w' * x; % Filter output

end

% Plot the results

figure;

subplot(3, 1, 1);

plot(audio);

title('Original Audio');

xlabel('Samples');

ylabel('Amplitude');

subplot(3, 1, 2);

plot(noisy_audio);

title('Noisy Audio');

xlabel('Samples');

ylabel('Amplitude');

subplot(3, 1, 3);

plot(filtered_nlms);

title('Filtered Audio (Adaptive NLMS)');

xlabel('Samples');

ylabel('Amplitude');

% Buttons for playing audio

uicontrol('Style', 'pushbutton', 'String', 'Play Original', ...

'Position', [20 20 100 30], ...

'Callback', @(~,~) sound(audio, fs));

uicontrol('Style', 'pushbutton', 'String', 'Play Noisy', ...

'Position', [140 20 100 30], ...

'Callback', @(~,~) sound(noisy_audio, fs));

uicontrol('Style', 'pushbutton', 'String', 'Play Filtered', ...

'Position', [260 20 100 30], ...

'Callback', @(~,~) sound(filtered_nlms, fs));

end

function [audio, fs] = getAudioInput()

% Function to get audio input from user

choice = menu('Select Input Method', 'Record Audio', 'Load Audio File');

switch choice

case 1

% Record audio

fs = 44100; % Sampling rate

duration = 5; % Recording duration in seconds

recObj = audiorecorder(fs, 16, 1);

disp('Start speaking...');

recordblocking(recObj, duration);

disp('Recording stopped.');

audio = getaudiodata(recObj);

case 2

% Load audio file

[filename, pathname] = uigetfile({'*.wav', 'WAV Files (*.wav)'}, 'Select an Audio File');

if isequal(filename, 0)

error('No file selected.');

end

[audio, fs] = audioread(fullfile(pathname, filename));

otherwise

error('Invalid choice.');

end

% Normalize the audio

audio = audio / max(abs(audio));

end

function [freq, magnitude] = analyzeSpectrum(signal, fs)

% Analyze the frequency spectrum of the signal

N = length(signal);

freq = (0:N/2-1) * (fs / N);

fft_spectrum = fft(signal);

magnitude = abs(fft_spectrum(1:N/2));

end

function M = determineFilterOrder(freq, magnitude)

% Dynamically determine filter order based on signal spectrum

peak_freq = freq(magnitude == max(magnitude)); % Find the dominant frequency

if peak_freq < 1000

M = 32; % Low-frequency dominant signal

elseif peak_freq < 5000

M = 64; % Mid-frequency dominant signal

else

M = 128; % High-frequency dominant signal

end

end

function mu = determineStepSize(magnitude)

% Dynamically determine step size based on magnitude distribution

energy = sum(magnitude.^2);

if energy < 0.1

mu = 0.01; % Low-energy signal

elseif energy < 1

mu = 0.1; % Medium-energy signal

else

mu = 0.2; % High-energy signal

end

end

[Mathieu NOE]

hello

I am not sure these algorithms are the best choice for audio denoising (without some artifacts including original signal distorsion).

Have you looked at wavelet denoising ?

Wavelet Interval-Dependent Denoising