# How to remove the AWGN noise from data?

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Let's say we have a vector data Uo=[20 30 40 50];

If we add AWGN noise to it, it becomes data U i.e.,

U=awgn(Uo,30);

Now we see that U and Uo are different. We want to get back our original data Uo. I tried as:

Uo=U-awgn(30);

But it gives error as:

Error using awgn (line 63)

Not enough input arguments.

What commands should I use to get back my vector Uo?

##### 0 Comments

### Answers (2)

Chunru
on 30 Sep 2022

Uo=[20 30 40 50]; % signal

U=awgn(Uo,30) % add noise to signal

% Uo=U-awgn(30);

% if you don't know the noise (which is U-Uo), you are not able to fully

% recover the signal.

% However, it is possible to "filter" out noise if signal and noise are

% different in certain characteristics.

% For your case, signal is a low-pass signal and lowpass filter can help to

% remove some noise.

Uo = [20:1:100]/30;

U = awgn(Uo, 10);

b = fir1(20, 0.02); % low pass filter

Ufiltered = filtfilt(b, 1, U);

t = 0:length(Uo)-1;

plot(t, Uo, 'r', t, U, 'b', t, Ufiltered, 'k')

legend("Signal", "Signal+noise", "Filtered")

##### 2 Comments

Chunru
on 30 Sep 2022

The plot is for u to see how good the filtered result as an approximation. You can always comment it out when you are satisfied the results.

For filter to work. You need sufficient data. If you have only 4 points, you may not be able to do much with the added noise.

Star Strider
on 30 Sep 2022

##### 15 Comments

Star Strider
on 3 Oct 2022

My pleasure!

It is likely not possible to completely recover a signal that has had Gaussian white noise added to it.

Experiment with the sgolayfilt function and wdenoise (wavelet denoising) function. Those are likely the best options.

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