How to Add random noise to a signal

hello all

please can ou help me out adding a noise signal to my system.

i tried adding a sinus function , but i would like to add a random noise signal rather than the sinus function. I'm running simulation from 1 to 3000

if k>1000 & k<2000

dk(k)=sin(12*k*pi*ts);
x=A*x+B*u(k)+B*dk(k);
else
dk(k)=0;
x=A*x+B*u(k);
end

Thank you so much

Best regards

[chris matthew]

how to add noise to audio not for signal

[Image Analyst]

What does that mean? Audio IS a signal. You can't add noise to audio without adding it to the signal that defines the audio waveform.

Answer 1

[Thorsten]

 x = linspace(-2*pi, 2*pi);
 plot(sin(x) + 0.5*rand(size(x)))

[lady bird]

Thank you Thorsten for your answer. this will create a noisy sinus function. but i'd like rather a noisy signal which doesn't have to be a sinus funtion, may be a white noise signal. but i dont know how to do that.

Regards

[Thorsten]

 noisy_signal = rand(1, 100); % Create noise-only signal.
 % Now add the noise-only signal to your original noise-free signal to create a noisy signal.
 noisy_signal = noise_free_signal + amplitude * rand(1, length(noise_free_signal));
 % Adjust amplitude to control the amount of noise.

[Tuhin Choudhury]

Hi Thorsten,

For your example:

 x = linspace(-2*pi, 2*pi);
 plot(sin(x) + 0.5*rand(size(x)))

I wonder what happens when your sin(x) has a very small magnitude (of the scale 10^(-5)). I am guessing the noise would not be scaled in that case leading to 10^6 highly amplified 'noisy signal'.

One way is to manually scale the noise w.r.t the input signal. However, for a signal with largely varying amplitude, what would be the workaround?

Thanks!

[Image Analyst]

Tuhin, you can have the amplitude vary with the signal amplitude if you want. For example

 % Create noise-only signal.
 noisy_signal = rand(size(noise_free_signal)); 
 % Create an amplitude for that noise that is 10% of the noise-free signal at every element.
 amplitude = 0.1 * noise_free_signal;
 % Now add the noise-only signal to your original noise-free signal to create a noisy signal.
 % Be sure to use .*, not *, so that you do element-by-element multiplication.
 noisy_signal = noise_free_signal + amplitude .* rand(size(noise_free_signal));
 % Adjust amplitude to control the amount of noise.

Now the noise - the max possible noise amplitude - will vary according to the noise-free signal amplitude. Of course since it's noise, the noise won't always be the max possible, it will be less, but it could potentially get that high.

[Tuhin Choudhury]

Hi,

Thanks. This would be more of a flexible scaling of the noise w.r.t the input signal.

BR- Tuhin

[Enac]

Hi,

This is a great solution. I want to point a subtle improvement. Using this algorithm you would end up with a noisy signal that is always above the original one. This is because rand() gives random numbers ranging from 0 to 1.

Usually, when you want to add noise to a given data you want the noisy function to be centered in the original. To do so you just need to generate random numbers going from -1 to 1. Simply replace

rand(size(noise_free_signal))

with

2*(rand(size(noise_free_signal))-0.5)

Answer 2

[Image Analyst]

So just use rand() instead of sin().

[lady bird]

i've been reading about this. and i'd like to add a white noise signal. but i really dont know how to do that.

moreover if i have to use the rand() fct you proposed what shall i put between parantheses?

thanks

regards

[Image Analyst]

Try it this way:

% Make up some parameters to get sample data
numElements = 3000; % Whatever...
B = 1; % Whatever...
A = 1; % Whatever...
u = ones(1, numElements); % Whatever...
x = 7 * ones(1, numElements); % Whatever...
% Main code here:
x = A * x + B * u;
% Add noise only between elements 1000 and 2000
noiseSignal = rand(1, numElements);
x(1001:1999) = x(1001:1999) + B * noiseSignal(1001:1999);

[Prajakta Yeola]

Can we use the same code if audio signal is .wav file? i.e. if x is a .wav file

[Image Analyst]

Sure, just figure out the amplitude and add it

yNoisy = yOriginal + amplitude * rand(1, length(yOriginal));

Answer 3

[KL]

Did you check the gaussian noise function?

[lady bird]

i found a awgn function but i dont know how to use it in my case?

[KL]

There's a difference between wgn() and awgn(). With the latter, you add noise throughout the whole range. I understand you want to add noise between certain time intervals. So in this case, I would suggest to use wgn(). At the moment I do not have the toolbox to use this function. Anyhow you shall use this function to calculate the noiseSignal variable according to @Image Analyst's code.

Answer 4

[Aparna Gupta]

Can anyone please help me with the code to add awgn noise to an eeg signal,which i have taken from a database and the file is of .mat type?

[Image Analyst]

Yes, probably. You can post the code in a new question.

[Alper]

xn=awgn(x,20), SNR=20 dB

Answer 5

[Mohammad Sohail Khan]

t = 0:pi/100:40;
x = cos(pi/10*t)+0.5*randn(size(t));
plot(t,x)

Then you know where pi/2, 3pi/4 etc are.

Answer 6

[Adewale Obaro]

N = 1000;
t = 0:1/N:2;
x = sin(2*pi*5*t);
Noise = x + randn(1,N)';
plot(t,Noise);
title('Noise in the Amplitude interval (0,0,1,0)');
ylabel('Amplitude [m]')
xlabel('Time [s]')