Searching sinusoid buried in noise

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Jurij Lorenzo Mazzola
回答： Image Analyst 2018-12-19
I have to find sinusoid completely buried in white noise. There are a lot of sinusoidal component in my signal, it is simple to find the 3 most strong, but the aim of the problem is to find the sinusoid whose spectrum is hidden in the spectrum of the noise. I tried so hard with periodogram, welch method, undersampling et cetera, but nothing. I cant improve SNR too in order to amplify the signal i want to amplify.
If someone want to try, I has attached the function. Unzip and copy in the current folder of matlab. Use in place of xxxxx the input 868270.
This is a function which has 868270 as input, returns a signal with much sinusoid hidden in noise. I succeed in finding almost 3 components.
Thank you very much for your attention, forgive my brutal english.
P.S. Sinusoids DO NOT last for the entire duration of the signal, they come and vanish.
  2 个评论
Image Analyst
Image Analyst 2018-12-17
What was the problem with using the frequency of the greatest strength to identify the dominant sine wave? It seems like that should work. Also, could you upload some screenshots?
Jurij Lorenzo Mazzola
Jurij Lorenzo Mazzola 2018-12-18
编辑：Jurij Lorenzo Mazzola 2018-12-18
The actual task of the problem is to find the more sinusoids we can. For sure some sinusoids are under the noise (in frequence domain).
Results with fft (the pic on he bottom) is graphics of: on the left the signal, on the right the fft diagram. as you see ther are no problems eithwiththe strongest sinusoids.
Resultswith periodogram (the pic on top) otherwiseshows, on the left the signal, on the right periodograms of different subsequence of the signal. As you see sinusoids are limited in duration, in fact in the first subsequence the is a a powerful component. forgive the ugly layout of the post but it seems it is difficult to post from mobile phone.

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回答（2 个）

Sarah Crimi
Sarah Crimi 2018-12-19
If you know what the sinusoids are that you want to look for, you could used a matched filter.
Image Analyst
Image Analyst 2018-12-19
Not sure what you mean by "as you see ther are no problems eithwiththe strongest sinusoids". From what I see, there ARE problems and only the first/top spectrum has a signal that you can confidently identify as a sinusoid. The rest are just so noisy that any real signal in there is totally swamped with noise and not recoverable. Not sure how you're measuring these signals, and if they're real world, or something you just made up. Perhaps you can use a Lock-in Amplifier.

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