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But dB is not a unit, it is a multiplier. dB on its own is unitless and if we say "X is reduced by 6 dB" you know that the value of X is half of what it was before (×0.5) if something is amplified by 6 dB it is double of what it was before (×2.0)¹

Note that the unit only starts to play a role when you reference your dB value to some absolute maximum, e.g.:

  dBV which is referenced to 1V RMS
  
  dBu which is referenced to 0.775V RMS (1mW into a typical audio system impedance of 600 Ohms)  
  
  dBFS which is referenced to a digital audio maximum level (0dBFS) beyond which your numeric range would clip (meaning all practical values will be negative) 
  
  dBSPL which is refrenced to the Sound Pressure Level that is at the lower edge of hearing (0 dBSPL), this is what people mean when they say the engine of a starting airplane is 120dB loud

Now dB is extremely useful in all fields where your values span extremely big ranges, like in audio engineering, where the ratio between high and low values can easily have a ratio of 1:10 Millions. So unless you want people to count zeroes behind the comma, dB is the way to go.

When we think about the connection between analog and digital audio dB is useful because despite you having volts on the one side and bits on the other side a 6dB change on one side translates to a 6dB change on the other, the reference has just changed. If we had no dB we would have to do conversions constantly.

Going from multiplier x to dB: 20×log₁₀(x)

Going from dB to multiplier x: 10^(x/20)

If you use dB to describe the power of a signal that is slightly different (you use 10 instead of 20 as multiplier/divisor)

But you can see, dB is just a way to describe a unreferenced size change in a uniform way or to describe a referenced ratio. And then it would be good to know what that reference is. So if someone says a thing has 40dB you they forgot to tell you the unit.

¹ this is true for the amplitude of a signal and differs when we talk about the power of a signal, where 3dB is a doubling/halving.

▲ rocqua 2 days ago | parent | next [-]

> But dB is not a unit, it is a multiplier. dB on its own is unitless.

The point of the article is exactly that this should be the case. But it ends up not being the case. Mostly because people use dB with reference to some assumed baseline. But also because a 20db change could be a 10x change conpared to baseline, or a 100x change compared to baseline, depending on what unit you are measuring in.

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mikewarot 2 days ago | parent | next [-]

20 dB is always the same, actually. If you multiply voltage (and thus current as well) by 10:1 (20 db) the power is multiplied by 100:1 (also 20 dB)

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rcxdude 2 days ago | parent [-]

That's the point that's confusing. Especially in contexts where it's not obvious whether it's power-like or amplitude-like. It should be 40dB of power gain or 20dB of amplitude gain, with the context made explicit.

	▲	mikewarot 12 hours ago \| parent [-]
		I don't see how it's confusing. Thanks to the scaling of voltage dB, you never have to worry, 10 dB of voltage gain is the same as 10 dB of power gain.

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atoav 2 days ago | parent | prev [-]

Yes but my conclusion would not be that Decibels are ridiculous, but that "People don't understand Decibels".

Decibels are okay. They are useful. They work. The problem is that people use referenced decibel values without adding anything that would allow us to understand which reference was used.

Maybe one could have come up with a better numeric way of doing the same thing (I am missing a proposal for this in the blog post), but then you'd have the XKCD-yet-another-standard problem. Everything uses dB for ages now, so dB it is or you need to convert between one and another all the time.

As an audio engineer I have no issue with dB as a unit. It is much better than using raw amplitude numbers.

▲ roelschroeven 2 days ago | parent | prev [-]

> If you use dB to describe the power of a signal that is slightly different (you use 10 instead of 20 as multiplier/divisor)

This is the part I don't get. This is the part where "dB is just a multiplier" falls short. It's there to "so that the related power and root-power levels change by the same value in linear systems" (that's how Wikipedia formulates it). Why is that even something you would want? Isn't it much more logical, intuitive, consistent and useful to reflect the fact of power being proportional to the square of the signal in it having double the dB value?