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Suppose I have a recorded sound, from which I can calculate a power spectrum, along with the Received Level of that sound measured in dB(A).

Is there a realistic way to back-calculate the non-weighted Received Level? Or does the A-weighting completely distorts everything?

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    $\begingroup$ Please edit the main title so it is a specific question. As it stands, your title is a short phrase that doesn't let readers know what information you're looking for. See guide for: "How do I ask a good question": stackoverflow.com/help/how-to-ask $\endgroup$
    – ASimonis
    Commented Jul 28, 2022 at 22:33

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The dB(A) levels are derived from the power spectrum, so if you can calculate the power spectrum then you do not need to back-calculate, you already have the power spectrum.

If, however, you have not the power spectrum (contrary to the statement in OP) but only the dB(A) spectrum, then you can obtain the power spectrum by subtracting the relative dB(A) weighting levels from dB(A) spectrum.

If you have only the broadband dB(A) reading, you cannot go backwards, as the integration (dB(A) filter) has already be done.

Edit: a related question can be found here: https://electronics.stackexchange.com/questions/173989/convert-db-a-to-db-spl, but contrary to that question the OP here assumes to have the power spectrum available.

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