In a signal like in spectroscopy, where a base broadband signal is overlaid with narrow peaks, what is the best way (without prior knowledge of the shape of the baseline) to compute the baseline? I have multiple datasets with different peaks, but which should have a similar baseline. If someone could point me to Matlab resources for this, it would be great.
The usual way is to have a percentage of the overal energy as a 'noise-level' threshold.
The threshold depends on how rich your spectrum is as well as your signal-to-noise ratio. Start with 10% and then experiment a little.
Dear colleague,
first, as I have stated at Research Gate, you can try our webpage http://amber.feld.cvut.cz/selective%20transforms/default.htm
and download the Approximate Discrete Zolotarev Transform package.
Second, if you do not get the results you have expected, send the data to me or to my co-workers in the project - Pavel Sovka, Vaclav Turon, or Pavel Masa.
I was thinking in something closer to the idea explained by Fernando Schlindwein, but I guess could be interesting to compare this results with the ADZT algorithm developed by Miroslav and colleagues.
Miguel, could you give us how were the results for both aproximations? At least qualitatively. That could be interesting.
Hi,
First, thank you all for your suggestions.
I realize that probably I formulated the question incorrectly: the data is from X-ray scattering, it isn't in time domain, so the term spectrogram is not correct.
I have looked at ADZ, which is very interesting, but not for what I want.
I ended up doing a fit to a combination of several Gaussian curves, using the curve fit tool (cftool) in Matlab, with good results. From the result I can select the wider peaks to reconstruct the baseline.
The attached image synthetic_spikes.png illustrates the type of data.
(I won't post the real data because it is unpublished work of a colleague)
If the frequencies of your narrow peaks and your baseline signals are very disparate, you could easily separate them using wavelet decomposition. You probably wouldn't even need to be too choosy with the parameters given the signal that you posted. The peaks should be separated from the baseline by several wavelet bands. Matlab has some very good wavelet tools.... looking up wavemenu will give you an idea of what it can do.
You could also use the MATLAB function "polyfit" for polynomial curve fitting (see attached MATLAB function)
Agcaer, the problem with your approach is that, since it doesn't take into account the peaks, it gives a slightly larger value for the baseline. Although I am not sure it is valid to model the baseline as a Gaussian, it seems to fit the data more closely - as in my image above - the only difficulty being determining the number of peaks. I didn't try the wavelet, yet.
If all you want is to eliminate the peaks and keep the baseline, just apply a median filter. Experiment with the threshold and width of the filter to get good results. Prior location of the peaks is not necessary.
Dear Dr. Miguel,
In your case you could do first a non-parametric spectral analysis and them a parametric spectral analysis.
I do have (MATLAB) packages that can handle all these things, in a very nice way.
If you are willing to talk about it, please contact me.
Regards,
Lucas.
Dear Miguel, I don't have a computer file for my computing
polygon fill-lines paper, sorry. But you may enjoy loooking at
mlab at www.civilized.com
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