Tuesday, April 16, 2013

Understanding Decibel Measurement Systems

Decibel-based logarithmic measurement systems are confusing. Not long ago, I wrote a post and produced an associated video to teach people about sample sizes, sample frequency, binary, and how it all relates to sound. That was part six of my Basic Audio Recording tutorial series on YouTube. I also have another post and video (numerically, the next in the series after this) that will talk about the Nyquist theorem, anti-aliasing, quantization noise, Fletcher-Munson curves, and dithering. Today, I have a post and video to delve more deeply into various decibel systems. This post is directly related to video #08 in my Audio Recording tutorial series, which is embedded below.

Although watching the video is the best way to learn about this topic, because of my illustrations on the whiteboard, I've also put a copy of the audio portion of that tutorial video on SoundCloud, for people who would like to download it to listen to in vehicles, while travelling, etc. Here's the audio-only version:

What Are Decibels?

The decibel is the unit used to measure the intensity of a sound. The human ear is incredibly sensitive. Your ears can hear everything from a light wind rustling through distant trees, to a loud jet engine, and they need to be able to process sounds appropriately. The decibel system is a logarithmic system that is appropriate for exponentially variable sound levels. Incidentally, decibels are also used to measure a large number of other logarithmic-based scales, such as power and voltage levels.

The first need for a decibel system came about many years ago, when telephone companies were trying to measure losses and gains across power grids. They decided to come up with a type of measurement that they named the Bel, in recognition of Alexander Graham Bell's work with early telephones. The decibel is one tenth of a Bel, and is abbreviated dB.

Decibels measure a change in power. Power is the change in energy in a system over time, and is best measured on a logarithmic scale. The range of difference in power levels between the quietest sound that a human can hear and the loudest sound before passing the threshold of hearing and reaching the threshold of pain is about one trillion times, or 10 to the twelfth power! That's a huge difference in scale.

Logarithmic scales are very interesting. Decibel systems are designed so that linear changes in the measurement units (ie. decibels) reflect exponential changes in power levels. Adding to the complexity is the fact that since the ear perceives different power levels on a different logarithmic scale than decibels (perhaps around Log 2, rather than Log 10), we get some very strange mathematical relationships. For example, consider these:

2x power = +3 dB = "slightly louder"
10x power = +10 dB = "about twice as loud"
100x power= +20 dB = "about four times as loud"
1000x power = +30dB = "about eight times as loud"

There are both similarities and differences in the ways that we perceive sound and light. Both are measured by our senses. However, light is a type of radio wave, and sound propagates through a medium in a wave-like pattern due to the oscillation of adjoining molecules. Therefore, light travels at an almost constant speed, whereas sound propagates more quickly when the medium that it is passing through becomes more dense.

Another interesting tidbit is that the difference in power levels between light and sound, as we perceive them, is not similar. With sounds, we can hear a difference between power levels of twelve orders of magnitude, as mentioned above. With light, the difference is only about three orders of magnitude. If you were to take the dimmest possible light that our eyes can see, and increase the power by only one thousand times, it would be at a level approaching the threshold of pain, causing retina damage.

It is also interesting that the power levels in light are much higher than in sounds. The very dimmest light that we can perceive produces about one watt of power. The very loudest sound that we can hear before approaching the threshold of pain produces about one watt of power. If you were able to instantly turn the power output from a 100-watt light bulb into purely sound energy, it would almost certainly deafen you, and possible cause serious injuries to some parts of your body.

In the embedded video (above), I cover the basics of a number of different decibel-based systems. For example, the following are all somewhat related to sound:

dB PWL - decibels power level
dB SIL - decibels sound intensity level
dB SPL - decibels sound pressure level
dBFS - decibels full scale
dBv or dBV - two types of decibels voltage, which use different reference levels
dBu - another type of voltage system
dBw - a type of power measurement

The Digital System for Decibels at Full Scale (dBFS)

Many decibel systems appear to have levels from 0 dB and upwards. However, this can be misleading, since decibels are a ratio, not an absolute quantity. So 0 dB in any system doesn't mean "nothing," it means that you're at the reference level, whatever that happens to be in that particular system. And it is possible to have negative decibel measurements in all systems. You just need to have a quantity or level that is lower than the reference level. Decibels are essentially a ratio.

In digital audio, in an audio editor system, the decibel levels are especially confusing. The dBFS scale starts with the reference level at the top, ie. the highest value. Any signal which is stronger than the reference level is a type of digital distortion. All other signals are measured in negative decibels, going down towards the noise floor.

Because of the special relationship between voltage and power, whereby voltage changes squared are in a direct relationship to power, the effect is that in a voltage system, a 6 dB increase means a doubling of the level, and a 6 dB decrease means the level is cut in half. In a 16-bit system, it is only possible to cut a signal in half sixteen times, going down 6 dB with each reduction to 50%. Therefore, a 16-bit system has a noise floor of -96 dB. In contrast, a 24-bit system has eight extra bits, and the noise floor is eight "levels" (of 6 dB each) lower, or around -144 dB. With a lower noise floor in a 24-bit system, there is a better potential dynamic range, and a more desirable signal-to-noise ratio. Of course, even that gets complicated, because you must differentiate between instrumentation noise and physical/external noise.

Does louder translate to "better" or "worse," and why? Well, humans usually perceive louder sounds to be better sounding. I don't know why. Maybe it's an evolutionary thing or an inherent biological preference - our brains just naturally prefer sounds that are easier to hear? Some audio engineers use this characteristic to their advantage, for better or for worse. In terms of producing music, an audio engineer will often try to increase the average volume level of a song through the use of compression, to make it sound "better" than other songs played around it. Unfortunately, the race to over-compress music has resulted in a loss of dynamic range in a lot of modern music.

Parting Words

Obviously, I’ve covered these subjects in a fairly superficial manner. If you watch the embedded video, I've covered all of these things in much more detail, so hopefully that will give you a lot of additional insight. Now you know the general theory behind these subjects, and why they're important to audio engineers. If you want to do further research on your own, I’ll put some links here now. Be forewarned! The physics and mathematics behind logarithmic systems can be pretty intense!

Links to other articles about Decibel systems:

If you’ve read all the way through this, you obviously want to learn more about audio recording and music production work. I don’t have a ton of written tutorials like this online, but I do have quite a few detailed YouTube videos that you might enjoy. I've got an organized list of those videos in the index of my "videos" page on my main website. If you're interested in any of those topics, you should bookmark this page right now:


Thanks for your interest in this series, and thanks for sharing this post or links to any of the videos.

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