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According to definition of decibel it’s “logarithmic unit of measurement used to express”

So in audio we often convert linear value from range 0 to 1 to logarithmic scale for example like that:

double result = 20.0 * log10(valueInRange_0_1);

(of course we need to menage situation when valueInRange_0_1 = 0, but leave it now, it’s not the case)

So for example for valueInRange_0_1 = 0.5 result will be about -6 and we can call it “-6 decibels”.

But the question is how we can call valueInRange_0_1 = 0.5:

“0.5 OF WHAT” ?

I know in audio we can call it “0.5 gain”, or “0.5 of linear value”. But is there any general term to use as opposite to decibel?

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    $\begingroup$ hi pajczur, in my private opinion your question is borderline, but on-topic. However, half of the text was unrelated discussion and preamble; if you want to discuss on-topicness, you're more than welcome to do so on meta.dsp.stackexchange.com! $\endgroup$ – Marcus Müller Dec 31 '18 at 0:00
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    $\begingroup$ But to address your point: that's really just 0.5. Not "0.5 of WHAT", just one half. You seem to be from an audio background: there's units like dBA that actually specify of WHAT you're talking. Decibel alone is, intentionally, only used for dimensionless entities. $\endgroup$ – Marcus Müller Dec 31 '18 at 0:02
  • $\begingroup$ "Gain of 0.5" is correct for any kind of signal processing I can think of. I'm not sure what context you think this would not be correct. You can also say "Gain of 0.5 V/V" if you need units. I also use the times symbol as a unit, like "0.5×". $\endgroup$ – endolith Jan 30 at 20:29
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Most of the time, it's the ratio of a physical quantity to a reference. The reference can either be an industry standard (Example: dBSPL, dBm, dBu etc.) or some other suitable quantity (Example: voltage at the input of a filter).

"Physical quantities" in audio are things like pressure, volume velocity, particle velocity, displacement, voltage, current, force, etc. (20 log) or sometimes also power, energy, or intensity (10 log).

For example: a microphone measure "sound pressure" as a physical quantity and to make it logarithmic you use

$$P = 20 \cdot log_{10} (p/p_0)$$

where $p$ is the original sound pressure, $p_0$ a suitable reference pressure, (20 micro Pascals is industry standard) and P the resulting sound pressure level in dBSPL.

Taking a ratio is very important, since it also takes care of the units. In digital signal processing, you often just deal with numbers (without units), but a proper choice of reference is still important. Typically choices are either digital full scale, some suitably calibrated physical quantity or just simply "1" . The reference is important: a dB value without a well defined reference (implicit or explicit) is meaningless.

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The numbers you are describing (normally encountered when programming audio) are unit-less. I think you could define them as a fraction of the dac's highest possible output (which is 1 or -1).
As an example, and assuming every other involved device has it's level set to maximum, a 1 of this unit-less number would push the speaker the furthest out it can go, and a -1 would pull it also the furthest in.

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