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What is a decibel? (tomhazledine.com)
78 points by mirceasoaica on Mar 22, 2017 | hide | past | web | favorite | 38 comments



A small nit-pick: >The highest possible level of sound produced by audio equipment is 0 dBFS.

...is only applicable to audio equipment operating solely on digital signals. Humans don't hear digital signals, we hear pressure changes, so at some point, those digital signals need to be transformed into analog voltage signals to drive pressure transducers (loudspeakers). Those analog voltages are measured by a different reference, a standardized voltage, as opposed to the absolute max of a digital scale. Analog voltages are commonly specified in dBV or dBu (0 references of 1 volt and ~0.775 volts, respectively).

The majority of the pro audio gear I've seen interacts with analog signals. So at some point in a piece of gear that handles both analog and digital signals, you're going to have to define a reference point between your digital and analog levels. This can vary from one piece of equipment to the next. The professional audio gear worth it's salt that I've seen can handle analog signal levels of +18dBu or more. Consumer and pro-sumer audio gear have lower limits, and can vary wildly. So 0dBFS signal going into your USB audio interface might come out as a +16dBu analog signal, while the same digital signal going into a professional mixing console might come out as a +24dBu analog signal.

Edit: Grammar and spelling


I have a question that goes into less detail. If such audio equipment defines the highest possible level as 0, then why is silence at ∞ instead of -∞?


That's a great point. The piece was written from a very web-centric point of view. Even though I used analogue mixing desks as my jumping off point, I only really looked at decibels in a digital context.

In fact, all the digital VU meters I've looked at do account for positive values, so I definitely shouldn't have breezed over that aspect so quickly.


This varies from product to product; for example, meters in Pro Tools are labeled directly in DBFS[1]. So are Yamaha digital mixers (at least the LS9 and M7 - not sure about the newer ones).

On the other hand, the Allen & Heath GLD has its meters labeled differently, and I'm not quite sure what they're referenced to (they go up to +12). This can be a bit frustrating, since I never know how close I am to digital clipping, but in practice I aim to get everything around 0 dB on the meters and I have at least 12 dB of headroom.

Wikipedia has a neat list[2] of different analog reference levels for 0 dBFS.

1: Pro Tools metering - http://i.imgur.com/YcUBR6H.png

2: https://en.wikipedia.org/wiki/DBFS#Analog_levels


"a dimensionless way to compare values that vary dramatically on a linear scale" ?

So many people totally omit the reference measure, which drives me abolutely batty, particularly when we're talking about sound.

In air, dB SPL is referenced to 20 micropascals. In water, it's 1 micropascal, so the medium matters.

Since loudness is a psychophysical percept, it's also dirty pool to speak of loudness in this way. Intensity can be quantified, loudness varies by listener.


So Spinal Tap could have been an even LOUDER band if they had used a smaller reference, say some fraction of a micropascal. Or even gasp 0 micropascals for INFINITE dB. Wow that must be so loud.


> Since loudness is a psychophysical percept, it's also dirty pool to speak of loudness in this way.

It's worth noting that there are standards for loudness as well.

For example: The FCC broadcast spec for commercials uses ITU 1770, which involves a filter. The resulting measurement is then labeled in units of dB LKFS. (LK are filter params, which are fixed by the spec, FS is full-scale, ie this is done digitally. (As an aside, video streaming could sure use some more uniformity for its inline commercials too.))


I've noticed very recently that Youtube started to play commercials louder than whatever I was watching. I don't remember google stooping to such tricks ever before,


Not saying you're wrong, but often the ads seem louder than the content without actually dissipating any more power; this is because ad studios are good at dynamic range compression and other sound engineering witchcraft.


> I don't remember google stooping to such tricks ever before

I kinda doubt that anyone has consciously tried to make the commercials louder than the content. It's a tough problem to get right: The television industry has been at it a lot longer, and they still barely make it work. The digital outlets still seem to be finding their footing on this issue.

FD: My biz delivers commercial content to TV, digital and cable outlets (and we normalize the audio). Normalization used to be a bit of a black art, but failure to get the audio levels right results in FCC fines to the stations, so you have to work hard to make it happen.


> I kinda doubt that anyone has consciously tried to make the commercials louder than the content. It's a tough problem to get right: The television industry has been at it a lot longer, and they still barely make it work.

right, that's why commercials are consistently louder than the "content".



Youtube plays commercials? ;-)


the Phon and Sone scales i'm familiar with. They're both based on pure-tone thresholds, though, so I'm not totally sold on their applicability to broadband sources.


Yes, in many fields there is an implicit reference measure that is never mentioned. In radio at least people write dBm to make it clear that it's relative to one milliwatt. But gains and attenuations are just dB, because the reference is irrelevant for a difference between two dB values with the same reference.


> But gains and attenuations are just dB,

Which is correct, because a gain is inherently unitless. It's a multiplier on an input signal strength. Likewise a signal/noise ratio is typically expressed as a pure dB measure. There are no units.


decibels aren't only used with reference to sound. For instance, I often use Vdb in the spectrum analyzer if subsequent harmonics are not linearly visible.

decibels are just a way to easily express ratios on a logarithmic scale. It's handy for all sorts of things.


That text mentions that dB is relative, but misses how the values are defined. A simple definition could be:

- If we are talking about dB in context of amplitude 6dB more means twice as much amplitude, 6dB less (or -6dB) means half the amplitude.

- If we are talking about dB in context of power 3dB more means twice as much power, 3dB less (or -3dB) means half the power.

dB is often also used to measure attenuation instead of gain. Here a positive dB value would actually mean less output compared to reference value.

And: For dB values often a suffix is used, to denote to what the value is relative to. E.g. dBV is relative to 1V, dbm is relative to 1 milliwatt.


What you said is kinda confusing so I'm gonna clarify

3dB = √2 which is the amplitude ratio which is equivalent to doubling the power, since power is square proportional to amplitude

6dB = 2, so a 6dB increase in power would be doubling the power, and a 6dB increase in amplitude would be 4x the power

a negative dB is just the reciprocal of the radio, so -6dB is equal to 1/2


> 6dB = 2, so a 6dB increase in power would be doubling the power

Pretty sure this part isn't right. Decibels are about power ratios, not amplitude ratios. 10 dB is a power ratio of 10, so 20 dB is an amplitude ratio of 10. 6 dB is a power ratio of 10^(6/10) ≈ 3.981 or an amplitude ratio of 10^(3/10) ≈ 1.995.), while 3 dB is a power ratio of 1.995 or an amplitude ratio of 1.413.

(It's probably sometimes defined so that 3 dB is a power ratio of exactly 2, making 30 dB 1024 instead of 1000.)


Yes I was wrong about the 6dB. That's a quadrupling of the power, not a doubling. It's twice the amplitude.

Unfortunately I can't edit my comment.


> - If we are talking about dB in context of amplitude 6dB more means twice as much amplitude, 6dB less (or -6dB) means half the amplitude.

> - If we are talking about dB in context of power 3dB more means twice as much power, 3dB less (or -3dB) means half the power.

Yes, and there's a reason for this relationship -- the two decibel scales (amplitude and power) are often interchangeable, because (in many contexts including sound waves in air and electrical waves in conductors) power varies as the square of amplitude. So the same decibel ratio can be used to express both amplitude and power.

https://en.wikipedia.org/wiki/Decibel


I'm reminded of my old boss's words when I worked as an EE at MIT Lincoln Lab. Whenever someone (self included) distinguished between the meaning of decibel on a signal's amplitude or power, he'd deadpan :

"A decibel is a decibel is a decibel".

Eg, a filter that attenuates a certain frequency by 24 dB is well defined. Regardless of whether you're interested in the resulting voltage or power of the output signal.

Of course for absolute terms a reference like dBm is used.


Great write up and balancing the relativity of decibels to frequency and environmental conditions is basically what audio engineers do all day.

In high school long ago I used to compete in Car Audio SPL competitions. Whenever we would compare notes about who has the highest readings, we would always reference spl at what frequency and where it was measured (windshield, kick panel or dash).

This is largely because in a pure SPL "Drag race" competitors typically compete on a single frequency rather than a song for example. It was instructive to compare frequency and spl because some cars resonant frequencies (fs) were better suited to different fs values of drivers (speakers) and then further down the line certain amplifiers optimized certain frequencies, down to understanding which MOSFETs they used.

So it was all about finding and matching the fs of your car, the drivers and the amps and then how much power you could push at once to make the whole system resonate the most optimally at a certain focal point in the car. Really mind boggling maths and physics when you really get down to it.

If anyone is interested in going deeper, John Hilliard did some amazing research into decibel understanding and managing SPL as part of the Apollo project. Basically he's the guy that made sure that the sound from the Saturn 5 engines didn't bounce off the deck and destroy the rocket on lift off.


Could you supply a reference for John Hilliard’s research?



All of that (which was quite interesting), yet he doesn't actually say what a decibel is. It is:

• 0.1 bel

• +/-1 bel = +/-10 dB = factor of 10 increase/decrease in power


Compare to the --at lest now, pretty obscure-- "Neper", which I've never seen used in practice except that I own a very old analog meter with a scale in Np...

https://en.wikipedia.org/wiki/Neper

The Np seems to have be used for amplitudes (rather than power), and value/ref = e^Np. And 0.01 Np ~ 1.01 (+1%) which is probably less useful than it seems at first glance.


The bel is never used in practice.

Although I am probably wrong, I always thought that "decibel" actually meant "decimal bel" because it represents a decimal logarithm and that the "bel" unit was devised as an afterthought to fit the SI prefix.

Still, it is a good way to remember that 10 dB = multiply by 10, because "deci" means 10.


> and that the "bel" unit was devised as an afterthought to fit the SI prefix.

It's named after Alexander Graham Bell, in 1928 at Bell Labs. https://en.wikipedia.org/wiki/Decibel#History (Yes I worked there, it was part of indoctrination training... :)

> because "deci" means 10.

Really, it means 1/10. ("Deca" is 10.)


> The bel is never used in practice.

Ah, but it is: https://www.hgst.com/products/hard-drives/ultrastar-he12 (click the "Specifications" tab and scroll down to "Acoustics")

(Hmm, this doesn't say what the reference level is. I guess it's 20μPa.)


So 'zero' is saying 'full power' and -10db is saying '10 times less power than full power' ?


yes, and -20dB is 100 times less power


Ossmann's 'Software Defined Radio with HackRF' lesson 3 - Decibel:

https://www.youtube.com/watch?v=J1FbhBqBYLM


The wikipedia article is also very informative. I recently had to learn about dBV (decibel volts) when trying to understand the spec sheet for a MEMS microphone.

https://en.wikipedia.org/wiki/Decibel


I got intimately familiar with that page and sources while trying to extend Boost.Units with Decibel support. Bit of a nightmare, in the end I just hardcoded in support for dBm?[VW]?


The sound of mysql crashing is about 10 decibels.


It's a tenth of a bel, right...? :-)




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