# Bit Depth and Dynamic Range



## crabman699 (Oct 31, 2010)

I understand that an increase in the bit depth will increase the resolution at which the sample amplitude can be calculated and stored. However, why does an increase in the bit depth increase the dynamic range, why doesn't it just increase the amplitude resolution and leave the dynamic range the same?


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## chonc (Jun 9, 2009)

The short answer is: that's the way PCM encoding works. But let me explain:

Sound is made primarily of two elements: Frequency (related to time) and amplitude (related to volume). For a digital device to store sound it has to convert it to numbers (which a computer understands well). To do this you have the analog to digital converter take a "snapshot" of a sound wave at a rate of 441000 times per second (for a CD) that will take care of the time element of the wave. At the same time the converter assigns a number for that snapshot that represents the amplitude (volume) of the wave at that precise moment. A 16 bit word consists of 16 ones and zeros assigned for that snapshot. 

There is so many combinations a 16 digit combination of zeros and ones can provide that number is the resolution you have (amplitude wise). You can now see that as more digits-per-word you have, the more resolution (steps) of gain you have at that precise moment.

You don't get more resolution frequency-wise because you scan the sound wave at a constant rate.

Hopefully this will clear up some of your doubts.


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## crabman699 (Oct 31, 2010)

Hi,

Thanks for the quick reply Carlos.

Yes I do understand all of what you've said, and I totally understand that fact that increasing the bit depth increases the amplitude resolution. But what I don't understand is why increasing the bit depth increases the dynamic range of the digital device as well as the amplitude resolution. e.g. a 16bit recorder has a dynamic range of 96dB, however, a 24bit recorder has a dynamic range of 144dB. How come the dynamic range doesn't just remain constant no matter what the bit depth is, and the resolution is the only factor that changes? 

Cheers

Chris


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## chonc (Jun 9, 2009)

well that is the way you hear resolution. It is much like the resolution of a digital photograph. The more resolution you have the bigger the photograph is because you have a more dense pixel count to represent an image.

a bit is just a step up or step down representation, the more bits you have the greater the range there is, and the greater the dynamic range the best "resolution" you have.

If the dynamic range would stay the same, then the perception of a higher resolution would be lost because the noise floor would stay at the same level of perception... 

hope this makes sense to you... anyway it is a very interesting topic.

Remember: this is the way PCM works, the way of representing a sound wave digitally is different in other formats such as SACD encoding (DST), and thus is the way a bit represents amplitude.


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## hakonfl (Feb 9, 2008)

It seems you have missed a bit in understanding what dynamic range actually is. 
In the digital domain, dynamic range is the _distance_ between peak level and the lowest sound possible to reproduce by a certain digital format. If the top level is the same for all bitdepth, then the lowest sound possible to recreate will be more and more quiet with increasing bith depth. 

In the analog domain, dynamic range is the distance between the omnipotent noisefloor and the loudest signal the equipment can handle (without distortion). 

Increasing the dynamic range of a digital file is not adding resolution. It adds distance to the quitetness....


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## Wayne A. Pflughaupt (Apr 13, 2006)

Hi Chris,

In truth both quantization and dynamic range are inseparable when it comes to bit depth. You indicated that you understand the quantization aspect, so I’ll concentrate on the dynamic range.

With pulse-code modulation (PCM) sampling, the bit depth is what determines dynamic range. The “rule-of-thumb” relationship between bit depth and dynamic range is, for each 1-bit increase in depth, dynamic range increases by 6.125 dB. So, 24-bit digital audio has a theoretical maximum dynamic range of 147 dB (6.125 x 24 = 147), compared to 96 dB for 16-bit. 

That’s the theory anyway. But if you’ve looked at the specs for any digital processors, you probably know none of them get anything approaching 147 dB dynamic range. This is because “real world” realities force limitations on both the analog and digital side of specifications. For example, if A/D converters were actually able to deliver a dynamic range of 147 dB, they would have to be capable of resolving signals as small as one billionth of a volt! Naturally, they can’t do that. In addition - down in this range transistors and resistors produce noise just by having electrons moving around due to heat. 

So even if A/D converters _could_ be designed and manufactured to resolve such low levels, the low-noise requirements of the other circuitry in the component - power supplies etc. - would be so stringent that they would either be impossible to build, or too expensive. 

What is the result of these real-world limitations? You’ve probably noticed the best dynamic range spec 24-bit processors can muster is between ~105-115 dB, _which is no better than what the best analog gear has to offer._

If a 115 dB dynamic range spec is the best digital gear can muster, why have they bothered to develop anything beyond 20-bit? Obviously for the luxury of ample headroom, which is where quantization rates comes into perspective.

It’s generally accepted in the professional recording field that once you’re above 16 bits, optimizing input signal levels is no longer an issue. This is because a 16-bit waveform, which has 65,536 amplitude or quantization “steps,” is considered the threshold of what is acceptable for hi-fi sound, because at that rate the human ear can no longer detect quantization errors at low levels. While there may be some debate about that in audiophile circles, a 24-bit waveform has over *250 times* more amplitude “steps” - 16,777,216. 

Why does that matter? Well, because a 24-bit waveform, even at -14 or -18 dBFS or even lower, will deliver dynamic range figures *and *low-signal quantization performance well in excess of 16-bit. What this gives us in the “real world” is miles of headroom. 24-bit A/D conversion gives us the luxury of more than 50 dB of “slack” before poor input signal levels start to take a toll on noise levels

Anyway - hope that makes sense.

Regards,
Wayne


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## crabman699 (Oct 31, 2010)

Yeah, that's helped a lot, cheers guys!


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## jaddie (Jan 16, 2008)

Wayne A. Pflughaupt said:


> ...<snip!> So, 24-bit digital audio has a theoretical maximum dynamic range of 147 dB (6.125 x 24 = 147), compared to 96 dB for 16-bit.
> 
> That’s the theory anyway. But if you’ve looked at the specs for any digital processors, you probably know none of them get anything approaching 147 dB dynamic range. This is because “real world” realities force limitations on both the analog and digital side of specifications. For example, if A/D converters were actually able to deliver a dynamic range of 147 dB, they would have to be capable of resolving signals as small as one billionth of a volt! Naturally, they can’t do that. In addition - down in this range transistors and resistors produce noise just by having electrons moving around due to heat.
> 
> ...


That's all very true, I've been griping about the so-called "24 bit" converters and their less-than-24 bit dynamic range for quite some time now. But, here's the exception, and no, you probably can't afford it:

http://www.stagetec.com/web/en/audio-technology-products/standalone-converter.html

Less than theoretical performance from real people's A/Ds aside, there are clear advantages for working in 24 bits and higher inside a DAW or DSP system. 

Jim


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