How can I add white Gaussian noise to my clean audio

 Fs = 14400; t = linspace(0,1,Fs); w = 2*pi*1000; s = sin(w*t); sound(s,Fs);

Answer 1

[Star Strider]

One option is to use the randn function to generate it.

 Fs = 14400; 
 t = linspace(0,1,Fs); 
 w = 2*pi*1000; 
 s = sin(w*t); 
 ns = randn(size(t))*0.1;                           % Gaussian Random Noise, Standard Deviation = 0.1
 sn = s + ns;
 
 figure
 subplot(2,1,1)
 plot(t, s)
 grid
 title('Original Signal')
 subplot(2,1,2)
 plot(t, sn)
 grid
 title('Original Signal + Noise')

 
 sound(sn,Fs);

.

[Haya AKKAD]

Hello @Star Strider, I have read alot of your old comments whish help me alot.. thank you!

Now I want to ask you help me to remove also Gaussian noise from this noisedMusic

I have done this try bellow but I think it is not the correct way because this is my first step with signal prossessing and matlab.

What I did is that I build designed filter:

[signal,fs] = audioread('noisedMusic.wav');
audiowrite('testfilter.wav',y, fs);
function Hd = myfilter
.
.
.
% Construct an FDESIGN object and call its BUTTER method.
h  = fdesign.lowpass('N,F3dB', N, Fc, Fs);
Hd = design(h, 'butter');
end

the result is not bad but I don't think that is the best way.

Thanks again

[Star Strider]

@Haya AKKAD — It is not possible to remove Gaussian noise (that is broadband noise) using a frequency-selective filter, since the noise is not bounded by frequency. The only way to reduce it in the Signal Processing Toolbox is with the Savtizky-Golay filter (sgolayfilt function). The only other way is to use wavelet denoising, wdenoise in the Wavelet Toolbox. It can likely not be eliminated using either method, simply reduced.

[Haya AKKAD]

Thank you very much, I will try

[Star Strider]

My pleasure!

A Vote would be appreciated!

[Haya AKKAD]

I vote for your answare but, I can't vote for comment, there is any way? @Star Strider

[Haya AKKAD]

Please @Star Strider I have 2 other question related to noise filtring:

1- the past filter I wrote (with butterworth), this work in frequencey domain that's right?

2- I have other way I learned it from a past comment for you, you work with cheb2ord & cheby2 and then with filtfilt.. my question is: is cheby work in frequency domain? and is filtfilt work in time domain? if that right then in total I can say that I filtered my audio in both frequencey and time domain? I am just confused...

[Star Strider]

@Haya AKKAD —

1 - No. All these filters work in the time domain. (Analogue hardware versions of them work in the frequency domain.)

2 - Those all work in the time domain as well. (I now prefer elliptic filters, as defined by ellipord, ellip, and zp2sos.)

To the best of my knowledge, only the fftfilt function operates in the frequency domain (although since everything in a computer is discrete or digital, and by definition uses sampled data, that definition is not absolutely correct).

So essentially everything in a computer is discrete and digital by definition. Only analogue hardware filters operate in the frequency domain.

[Haya AKKAD]

Again thanks alot,

My confusing come from when we put the Passband and Stopband so I thought we work in frequency domain..

[Star Strider]

My pleasure!

That is a logical assumption, and is essentially correct because that is how filters are defined and calculated. It would be entirely correct if this discussion was about analogue signals.

The filters were initially designed as analogue filters, and go back to the early days of radio engineering. When computers became avaialble, and with them time sampling of analogue signals to their discrete or digital representations, various methods for converting analogue filters to discrete or digital filters were developed, the most widely used being the Tustin or bilinear mapping (or transformation).

The essential idea behind digital filters is to compute the inverse Fourier transform of the analogue filter spectrum characteristic in order to create a representation of it in the time domain so it can be used with time domain signals (although in reality it is more complicated than that simple description).

[Haya AKKAD]

All right, you give me more than I expected in this helpful conversation. you deserve all the best

Thanks Again and good night

[Star Strider]

Thank you!

Answer 2

[Image Analyst]

Try this:

Fs = 14400;
t = linspace(0,1,Fs);
w = 2*pi*1000;
s = sin(w*t);
subplot(3, 1, 1);
plot(s(1:100), 'b-', 'LineWidth', 2)
grid on;
title('Original Signal')
noiseAmplitude = 0.2;
noiseSignal = noiseAmplitude * randn(1, length(s));
subplot(3, 1, 2);
plot(noiseSignal(1:100), 'b-', 'LineWidth', 2)
grid on;
title('Noise Signal Alone')
sNoisy = s + noiseSignal;
subplot(3, 1, 3);
plot(sNoisy(1:100), 'b-', 'LineWidth', 2)
grid on;
title('Noisy Signal = Signal + Noise Signal')

%  sound(s,Fs);