There must be information on the desired signal itself, and/or the distribution of the noise (e.g. Gaussian). Kalman filtering can be used in this view, in that it provides a model of the signal, and it is possible to recursively reduce noise by improving signal estimate at each step.

Still, higher order statistics can be used to discrimintae when statistics of noise is known.

thank you Ismail.

I have tried using the moving average algorithm.....the results in time domain was fine....can this be done with median instead of the mean.

Furthermore, according to you how can I discriminate the noise to know its statistical properties.....and also what type of higher order statistics can be utilized.

I am looking forward for working with statistical exploration of signals.

Thank You once again.

Higher order spectra, which are

Fourier transforms of cumulants, are used usually in this respect. Again, Gaussian signals have all their cumulants zero, so these may be used to separate Gaussian noise from non Gaussian Signal. Other properties are symmetry, flatness (described by fourth cumulant, kurtosis) and higher order shapes are used.

Thank you once again for your kind and prompt reply.

will definitely follow you up after going through your suggestions,

For Samantha,AK

I thing MA (moving average) method was generated noise too, because some information may be lost! And if we use Gaussian distributed we lost 0.05 information. I suggestions in wireless communication Kalman Filter is good for performance in BER vs S/N, there method include chi filter to resignation in digital communication. I hope this comment support to solution your problem.

@ Made Yadnya,

Of course you have provided an important solution to my problem.

You should explain the desired signal and application and also time limits. But generally you can use kalman filter, time- frequency filters (e.g. Wavelet) .

Hm, not sure if I get your post correctly. If you know the spectral characteristics of your signal and the spectral characteristics of the noise only, my first step would be to apply a Wiener filter. On the other hand, if you know the signal form, you could apply a matched filter.

You should use adaptive filter. The source of noise should be sensed, and be adapted to cancel the noise which is mixed with the desired signal

Correlation o matched filter...

Mr. Mauricio Icaran, i suggested we can use correlation o matched filter and how we do habit noise in sample signaling non stationer , for this problem what we do?

In sampling signal the reduction of the noise depend about what source codig your use....

White noise is easy to remove, you can use any low pass filter.

@saifi: I might lose some harmonics of concern.

@saifi: How many low pass filter we can do it for white noise for all band?

Some high pass filtering can be done.....but to eliminate noise from all bands its not very advisable.

But we practically do it in general cases.

By Maximum A Posteriori Filtering in each subband.

@alexandru isar: Do you mean implementation by kalman filtering?

or is there any other efficient filter to implement this.

There are other efficient filters to implement this, as for example the bishrink filter proposed by Ivan Selesnick.

@Alexandru Isar: Can bishrink filter be used in case of current signature analysis....?

And what documents should I follow for this filter?

http://www.tc.etc.upt.ro/cercetare/CNCSIS_Idei/al_doilea_an/Ioana_Thesis_ver2.1.pdf

THANK YOU very much.

It really helps. Hope It helps my cause.

In cases you do not have so much information about the signal, but noise is white gaussian and the signal somehow (mathematical conditions here) independent, there are efficient wavelet methods, for instance based on SURE: Stein Unbiased Risk Estimators. A quite general framework (including bishrink as suggested by Alexandru Isar) may be found in

A nonlinear Stein based estimator for multichannel image denoising, IEEE Transactions on Signal Processing, August 2008.

http://www.laurent-duval.eu/Articles/Chaux_C_2008_tsp_non_sbemid.pdf

If the variance of the noise is unknown, it can be estimated in the wavelet domain quite efficiently. You may have a look at Figure 4, here for images, but would work for signals as well;

Common denoising algorithms : wavelet-thresholding, empirical mode decomposition-detrended fluctuation analysis have shown particular good results in the same. You may try EMD-DFA. It usually yields a good performance in my experience. Best wishes

http://in.mathworks.com/matlabcentral/fileexchange/52502-denoising-signals-using-empirical-mode-decomposition-detrended-fluctuation-analysis

Hi Aditya,

Your answer is not fully correct. The methods that you mention are generally used for artifact removal and not white noise.

Forcing the noise singular values of a Hermitian data matrix (see originalDataMat) constructed from the data and then reconstructing the noise-free data matrix using SVD can help in reducing the overall noise floor (see spectrum.png). The noise was taken as white and Gaussian. The signal consisted of three frequency components with unity amplitude and random phase.

The signal + residual noise statistics is also preserved. This can be found from the auto-correlation of both the sequence (see autocorrelation.png).

The problem is the structure of the reconstructed data matrix (see reconstructedDataMat), is no longer Hermitian. Further discussion on preserving the structure of the data-matrix and reducing the white noise is welcome.

First you should calculate auto correlation of noisy signal values. Also, Calc. confidence intervals with ±2/sqrt(N-1), where N is samples number.

If output seems to have a delta Dirac form, then you can conclude that signal is a white noise one, on the other hand it is colored one.

That is to ensure whether the noise is white or colored. It is difficult to remove white noise completely. Optimal state estimators are know to extract the best possible information from an observation corrupted by white noise. However, the contention to remove the noise is till on!

In my case I have been dealing with this issue for a while, trying to remove short-term cyclicalities from economic variables (actually the problem is reversed, but you ill see you can use this thethod the other way around with a simple substraction). My test variable was the Norwegian Unemployment from January 1990 to February 2020 (March 2020 is not included as I didn't want to model the COVID situation). The method I have been using is by taking the Discrete Time Fourier Transform (DTFT) of my data sample. As you can see here https://stats.stackexchange.com/questions/121360/what-is-the-fourier-transform-of-a-brownian-motion the key point is that the square absolute value of the Fourier transform of a white Gaussian noise is inversly proportional to the square of the frequency. Hence, my solution was to search for the best fit of the absolute value of theTFT of my variable to a function of the form F = a + b/(w - w0). The next step was to obtain the normalization of the difference, d*, between the model and the real data as d* = (d - m)/s, being d the difference between the absolute value of the FT and the fit, m the average of the differences and s the standard deviation of the differences (this exercice birngs a series with average 0 and standard deviation 1). Following this step, I select a bias number (that I introduce manually) and whenever d* is higher than the bias I take the fit model and in the opposite situation I take the real data. The argument of the complex DTFT is kept untouched. The last step is to take the inverse DTFT. The reason of this process is that cyclicalities in any function are seen as peaks in the DTFT, so my aim was to remove these peaks and the result is pretty good, as you can see in the image. Im my case I also applied a bootstrapping method with a second order DTFT of the difference between the original data and the result obtained in time domain.

In your case, this method seems to be useful until obtaining the best fit of the white noise but, instead of using my approach to remove cyclicalities, I would substract the fit to the data you obtain. Also take into account that a direct substraction will lead to negative absolute values, so instead of a direct substraction a good idea might be to take a division. This is equivalent to doing a convolution that substracts the white noise from your data (just as an idea, as I've not tried this solution).

I hope you find this useful.

It is behavior natural instrument from input power and resistant. Noise is normal distribution, the have variation .