What sound level units range from -1 to 1?

Question

I'm used to using dBFS to describe audio levels, where 0 dBFS marks the audio level beyond which clipping occurs. This article that describes DC offset, however, notes that DC offset is characterized by excessive audio levels in either the positive or negative directions: http://en.flossmanuals.net/pure-data/ch025_dc-offset/

In what units is it describing audio levels?

Answer 1

This is not a sound level. It's a pressure level, or voltage level, or whatever physical sound transmission you're imagining.

DC offset is the absolute sample value of the average of all audio samples.

Plain sample values are also used to calculate peak levels, except that you don't average anything but take the maximum of the absolute values. Because the absolute value is never negative, you can then apply the logarithm to get the corresponding dBFS value; basically that's just a convenient but arbitrary transformation.

Some examples:

• A perfectly normalised audio file has a peak level of 1, and a DC offset of 0. Equivalently, the peak level is 0 dBFS and the DC offset -∞ dBFS. This means, the signal is "centered" around the baseline, and there is one sample that reaches either¹ value +1 or -1.

• A silent file has peak level 0 and DC offset 0, both -∞ dBFS.

• A file with only DC in it will have the same DC offset and peak, except the latter is always positive, but the DC offset may be negative.

• Real-world audio prior to normalisation will have peak depending on the gain, and very small DC offset – again, this may be positive or negative.

You can't, mathematically speaking, convert a negative value to dBFS, still this is sometimes done (you just take the absolute value like with peak, and perhaps denote the sign seperately). The formula is then²

v [dBFS] = 6 * log₂(v [abs])
v [abs] = 2^{v [dBFS] / 6}

I.e. reducing anything by 6 dB halves the amplitude of the quantity you're talking about.

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¹_{Note that generally, not both will happen: sound isn't "symmetric"! In a sound file that's not mastered to avoid such issues, the peak is normally dominated by a few "freak transients", that heavily swing in one direction. For a normalised, otherwise unprocessed drum track, you may well have positive extreme +1 but negative extreme only -0.6 or something like that.}

²_{Strictly speaking, the official definition is
v [dBFS] = 20 * log10(v [abs])
v [abs] = 10^{v [dBFS] / 20}
which gives almost exactly the same result. Base-2 is, in practice, a much more useful orientation than base-10, for audio production.}