How to remove the AWGN noise from data?

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Sadiq Akbar 2022-9-29

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评论： Sadiq Akbar 2022-10-4

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?

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Chunru 2022-9-30

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在 MATLAB Online 中打开

Uo=[20 30 40 50]; % signal

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

U = 1×4

19.9837 29.9773 40.0475 50.0504

% 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")

Thanks a lot dear Chunru for your kind response. Actually I want to get back my my original vector Uo if not exactly then aprroximately equal.I don't need the plot. In your piece of code, you have used a low pass filter. But I don't know why did you use it? 2ndly you have not get back the original Uo. Can you do some filtering so that we can get exactly or approximately Uo. 3rdly my original vector consists of only four values but you have taken 81 values i.e., Uo = [20:1:100]/30; Why is this?

Chunru 2022-9-30

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.

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Star Strider 2022-9-30

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I would simply use a moving average filter, for example movmean, or choose one of the options in smoothdata, to eliminate normally-distributed additive noise.

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Star Strider 2022-9-30

在 MATLAB Online 中打开

Getting your original vector may not be possible. It may be necessary to accept the result being ‘close enough’.

% clear all

% clc

% A template is given

temp = [20 30 40 50]';

% Create a matched filter based on the template

b = flipud(temp(:));%My comment:Just reverse the vector temp up side down

% For testing the matched filter, create a random signal which

% contains a match for the template at some time index

x = [randn(200,1); temp(:); randn(300,1)];

n = 1:length(x);

% Process the signal with the matched filter

y = filter(b,1,x);

% Set a detection threshold (exmaple used is 90% of template)

thresh = 0.9

thresh = 0.9000

% Compute normalizing factor

u = temp.'*temp;

% Find matches

matches = n(y>thresh*u);

% Plot the results

plot(n,y,'b', n(matches), y(matches), 'ro')

grid

% Print the results to the console

display(matches);

matches = 204

Check = y(y>500)

Check = 7×1

1.0e+03 * 0.9831 2.2866 3.7918 5.4000 3.8339 2.3067 1.0961

Also, the filter may need to be ‘normalised’, for example:

y = filter(b,sum(b),x);

I will let you experiment further with this.

Star Strider 2022-9-30

在 MATLAB Online 中打开

My pleasure!

Yopu are filtering a signal padded on both ends by normally-distributed random numbers. It is unlikely that you will be able to recover your exact signal from it. (I changed the filter call to experiment with a normalised version. Change it back if you want to.)

% clear all

% clc

% A template is given

temp = [20 30 40 50]';

% Create a matched filter based on the template

b = flipud(temp(:));%My comment:Just reverse the vector temp up side down

% For testing the matched filter, create a random signal which

% contains a match for the template at some time index

x = [randn(200,1); temp(:); randn(300,1)];

n = 1:length(x);

% Process the signal with the matched filter

y = filter(b,sum(b),x); % Changed

% Set a detection threshold (exmaple used is 90% of template)

thresh = 0.9

thresh = 0.9000

% Compute normalizing factor

u = temp.'*temp;

u = 5400

% Find matches

matches = n(y>thresh*u);

% Plot the results

plot(n,y,'b', n(matches), y(matches), 'ro')

grid

% Print the results to the console

display(matches);

matches = 1×0 empty double row vector

Check = y(y>mean(y(1:100))+10*std(y(1:100))) % Recover Peak Data

Check = 7×1

7.4727 16.5828 27.1003 38.5714 27.9014 16.9928 7.4240

Star Strider 2022-10-3

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.

Sadiq Akbar 2022-10-4

Thanks a lot for your kind response dear Star Strider. Can you demonstrate it here as I am not too much expert in Matlab?

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