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?

  • 1
    $\begingroup$ 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
  • 3
    $\begingroup$ 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

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.


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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.