# Re: getting a signal level from a signal+noise measure?

Hi Rochelle and all,
First you must go back to linear domain, forget the glossy dB domain for a second.
Under the hypothesis that your signal and noise are uncorrelated - hopefully that is true, the estimated absolute received power is the sum of the speech signal and noise variances. This comes from the mathematical expectation of the cross-correlation of speech and noise being zero.
So you end up with: A^2 + B^2 = C^2
where A is the noise standard deviation (square root of the variance), B is your speech rms amplitude, and C the resulting signal rms amplitude. Knowing C and A, you have a relatively good estimate of what B is.
Now you have your speech amplitude in dBrms: from 20 log10(B/B0) where B0 is 20uPa or whatever reference you find appropriate.
Hope this helps.
Eric.

-> I realize this would never be exact, but is there a
formula for mathematically subtracting out the dB level of the noise
level and then transforming this in such a way that one can get a
rough estimate of the amplitude level of the signal alone? (Or, is
there a mathematical function for dB that tells you what level A is
at if you know A+B and B alone?)

______________________________________________________
Eric Delory
Laboratori d'Aplicacions Bioacustiques
D164, Escola Politécnica Superior d'Enginyeria de Vilanova i la Geltrú
Universitat Politécnica de Catalunya
Avda. Víctor Balaguer s/n
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Barcelona, España.
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eric.delory@upc.es