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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: getting a signal level from a signal+noise measure?*From*: Eric Delory <eric.delory@xxxxxx>*Date*: Sat, 11 Sep 2004 18:55:24 +0200*Delivery-date*: Sat Sep 11 13:32:16 2004*Reply-to*: Eric Delory <eric.delory@xxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

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.

Answering Rochelle Newman:

-> 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

08800 Vilanova i la Geltrú

Barcelona, España.

Tel. (34) 93 896 72 27

Fax.(34) 93 896 77 00

H/P.(34) 655 33 0196

eric.delory@upc.es

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