Downsampling - The effects of ...........

[ISeekTheTruth]

Perhaps between neighboring bits of the same word. Still wondering about the __ db? above

 

[dc655321]

One last clarification. on dither and tearing. I am seeing posts that each bit ? has 6dB of dynamic range. There must be some context to this blanket statement.
View attachment 201171

No idea what “tearing” refers to.
A somewhat hand-wavy derivation of the 6dB/bit measure is here.

Also not clear what your diagram is trying to express. A 16 bit signal, re-encoded to 24 bits, has its noise floor extended quieter by 8 bits: it is not made louder by 8 bits.

 

[ISeekTheTruth]

Just wanted to know how loud in db 0000 0000 0000 0001 (16 bit) was above 0dB same for24 bit. 0000 0000 0000 0000 0000 0001 Tearing is the sound made due to bit reduction without dither on a fade out.

 

[ISeekTheTruth]

Guess this diagram is not very clear. What I meant was if we had a sine wave having a + and - 0000 0000 0000 0001 above and below zero. How loud would that be in dB compared to 0dB. ie how large is the noise created by dither in dB when moving from 24 bit to 16 bit?

 

[earlevel]

One last clarification. on dither and tearing. I am seeing posts that each bit ? has 6dB of dynamic range. There must be some context to this blanket statement.
View attachment 201171

Close enough that most people say 6 dB

Each bit doubles the range (7 bits give you 128, 8 gives 256...), so it's actually 20 * log10(2), about 6.02059991327962, or some would say 6.02.

To break that down, "2" is the ratio we're looking for (2/1); bels are a log ratio, so log10(power), then we want decibels (ten times bels) so it's 10 * log10(power). But we don't have power, we have "field"—the digital value is proportional to voltage, not power. We don't know the power, but audio is essentially into a constant resistance, so power will be proportional to voltage, which is proportional proportional to our digital value. Since decibels are all about proportion (ratios), that serves us just fine.

Specifically, power is proportional to voltage squared. So now we have 10 * log10(value^2). But we can pull the log10 of the power of 2 out as a multiplier, and get 20 * log10(value). Way more that anyone needs to know, but just in case you were thinking "why multiply by 20?", now you know.

 

[RayDunzl]

0001 = 1
0010 = 2
0100 = 4
1000 = 8
and so on...

to 01111111 or +32767 and 11111111 or -32768 in a 16 bit signed file.

Each is a doubling of the previous value.

The values represent voltage change.

Doubling, in this case, is 6.02dB increase.

 

[RayDunzl]

Guess this diagram is not very clear. What I meant was if we had a sine wave having a + and - 0000 0000 0000 0001 above and below zero. How loud would that be in dB compared to 0dB. ie how large is the noise created by dither in dB when moving from 24 bit to 16 bit?

Not all dB are the same "size"...

Bigger dB are bigger than smaller dB.

Doubling a large voltage may take the resulting sound from too loud to excruciating.

Doubling a tiny voltage may not even be noticeable.

---

16 and 24 bit have the same ultimate loudness the way it is implemented

16 bit has a nominal 96db range, and 24 bit has 144dB range.

But the difference is at the quiet end, not the loud end, and provides finer resolution (more exact values) along the way, which may or may not be audible.

The smallest bit of 16 bits is subdivided into 255 more levels.

 

[dc655321]

Tearing is the sound made due to bit reduction without dither on a fade out.

Ah. Those who think they know what they’re talking about call that Quantization Distortion.

Assuming dither is a full bit, then it would be -90dB for 16 bit signals and -138dB for 24 bit signals, for 0dB full scale.

 

[earlevel]

Guess this diagram is not very clear. What I meant was if we had a sine wave having a + and - 0000 0000 0000 0001 above and below zero. How loud would that be in dB compared to 0dB. ie how large is the noise created by dither in dB when moving from 24 bit to 16 bit?

It depends on the exact dither implementation and how you measure it, but in a nut shell, typically ± half bit (the target lsb), or a peak-to-peak amplitude of 1 lsb. That would be -90 dBFS for 16-bit, for instance. But it might make more sense to spec it as RMS, which would be about 3 dB less, ~93 dB.

BUT, don't forget this isn't really added noise, because trunction also has an error of ± half bit. So, you're not sacrificing anything (perhaps a very small amount more in terms of noise power), you're mostly rearranging the error so that it's not correlated with the signal (that is, the noise won't change depending on what the signal is doing, it will remain steady).

So...you can look to my first paragraph if your intent is to answer the question, "what is my minimum noise floor at the target sample size, assuming my recording was essentially perfect to begin with?". But if your intent is to answer the question, "how much noisier did I make it by dithering?", for practical purposes that is zero. (Noise shaping makes it even better in the region of most interest. Not that I think it's generally worth it.)

 

[RayDunzl]

Just wanted to know how loud in db 0000 0000 0000 0001 (16 bit) was above 0dB same for24 bit. 0000 0000 0000 0000 0000 0001 Tearing is the sound made due to bit reduction without dither on a fade out.

Your "0dB" is undefined.

But 0000 0000 0000 0001 would be the same loudness as 0000 0000 0000 0001 0000 0000 in 24 bit, assuming the same playback device.

 

[Keened]

Not all dB are the same "size"...

Bigger dB are bigger than smaller dB.

Doubling a large voltage may take the resulting sound from too loud to excruciating.

Doubling a tiny voltage may not even be noticeable.

This seems like an insane unit to use regularly then. Is there a distinguishing addition to the dB unit that is dropped for "convenience" because it seems like there are a lot of dB units used in Electro-Audio that aren't interchangeable?

 

[danadam]

Just wanted to know how loud in db 0000 0000 0000 0001 (16 bit) was above 0dB same for24 bit

The reference for digital signals is a full scale signal. Such signal is at 0 dBFS.

For 16 bits, 0000 0000 0000 0001 would be 90 dB below full scale, so that signal would be at -90 dBFS.

For 24 bits, 0000 0000 0000 0000 0000 0001 would be 138 dB below full scale, so that signal would be at -138 dBFS.

This also checks out as "1 bit is 6 dB" rule. 24 bits is 8 more than 16 bits, so it is 8*6 = 48 dB more dynamic range, and 90 + 48 = 138.

 

[dc655321]

This seems like an insane unit to use regularly then. Is there a distinguishing addition to the dB unit that is dropped for "convenience" because it seems like there are a lot of dB units used in Electro-Audio that aren't interchangeable?

Decibels, being a ratio of dimensioned quantities, are unitless.
The irregularity ("not all the same size") stems from a dB being a logarithm, which is non-linear.
At least, I think that is what Ray meant?

 

[danadam]

This seems like an insane unit to use regularly then.

It is no more or less "insane" than logarithms

Is there a distinguishing addition to the dB unit that is dropped for "convenience" because it seems like there are a lot of dB units used in Electro-Audio that aren't interchangeable?

"dB" on its own is a measure of a ratio between any two signals.

"dB" with a suffix is also a ratio, but now one of the compared signals is a signal at the reference level. For example:

• for dBFS the reference signal is a full scale signal,
• for dBV the reference is 1 Vrms,
• for dBu the reference is 0.7 Vrms,
• for dBSPL the reference is 20 uPa.

So for example, if you say the difference between two signals is 6 dB, it means that one of those signals is twice as big as the other *. If you say that some signal is at 6 dBV, it means that this is a 2 Vrms signal.

*) Note that it will be a bit different if we are talking about power quantities (see power vs field quantities)

 

[Keened]

Decibels, being a ratio of dimensioned quantities, are unitless.
The irregularity ("not all the same size") stems from a dB being a logarithm, which is non-linear.
At least, I think that is what Ray meant?

I just skimmed the Wikipedia page on Decibels and it seems that I'm not alone in the confusion it causes because it can be a relative or absolute reference, of different logarithmic bases, that may or may not be attached to different actual units (that are often unwritten because they are understood within the context of the industry using them).

 

[dc655321]

it seems that I'm not alone in the confusion it causes

Well, take some comfort in that I guess?

 

[RayDunzl]

I just skimmed the Wikipedia page on Decibels and it seems that I'm not alone in the confusion it causes because it can be a relative or absolute reference, of different logarithmic bases, that may or may not be attached to different actual units (that are often unwritten because they are understood within the context of the industry using them).

The way you hear loudness is not linear, someplace closer to logarithmic, in terms of the change in amplitude .

Whatever the volume, whatever you're ,measuring, whatever the absolute linear difference, 1db more is barely noticeable, 3db is a little louder, 6db is "can you turn it up a little more?", and 10dB is generally quoted as sounding twice as loud.

Just go with it. Somebody else did the work to figure it all out to make it useful for you, like most everything else.

---

Load a file into Audacity, and you can easily (well, I can) juggle the amplitude to get the hang of its effect on your earholes.

 

[ISeekTheTruth]

So the 6db approximate difference between adjacent bits in a 16 or 24 bit word makes sense. so the difference between 0000 0000 0000 0001 and 0000 0000 0000 0010 would be around 6 dB. I guess my original thought was in this post that 0dB was the base reference for the threshold of hearing. As you have indicated I should have been using full scale signal as my base reference for dB. Then your numbers of around -90 and -138 for a least significant bit toggle in a 16 bit or 24 bit word respectively make some sense. So as a passing comment, the noise added by dither IS extremely small. I also read that DA converters running at 24 bit are hard pressed to reproduce analog faithfully beyond 20 bits. Not sure if that is true or relates to the delivery to the air at the end of the day.

 

[earlevel]

I just skimmed the Wikipedia page on Decibels and it seems that I'm not alone in the confusion it causes because it can be a relative or absolute reference, of different logarithmic bases, that may or may not be attached to different actual units (that are often unwritten because they are understood within the context of the industry using them).

I understand why you say that, but better to realize It's always relative. It might be relative to what it was before ("the mix is getting close, but the kick is too loud—try dropping the kick 4 dB"), it might be to the maximum possible ("the peaks are running hitting -2 dB"—that can be a little vague, so it's best to say -2 dB FS or full scale, if that's what you mean), or an agreed reference level ("the output of this preamp can attain +18 dBu").

The bottom line is that you might need to understand dB a little if you want to make sure of what your equipment is best suited to work with what you've got (-10 dBV or +4 dBu gear, for instance—some gear let's you choose, but it's still a good idea to understand that these are simply a lower level swing or higher, "pro" level swing of voltage). Seriously, how much easier on your life would it be if they quoted voltage swing instead? Not much. And voltage isn't as useful when it's a different level—how much louder is a 0.84 V p-p signal than a 0.32 V p-p signal? But it's pretty easy to have an intuitive idea of how much louder a -6 dB signal is compared with a -16 dB signal, once you get used to it (doesn't take long). (Notice I didn't use a reference like dBFS or dBu on that last example, because it doesn't matter—the latter signal is 10 dB less that the first, and that's all you care about.)

People doing acoustic measurement work with dB SPL, but most people can ignore that. The fact dB is relative means that you can turn up the volume in your room so that it measures 10 dB SPL higher—a substantial increase—or you can turn up your mixer output 10 dB, and it's the same relative increase (assuming no clipping). And no math was involved in converting Voltage to Pascals, the electrical signal versus the sound pressure created by you speakers.

Lastly, true that it's not incredibly useful to an average listener. You buy home audio gear that has quality sound and gets as loud as you need it to get, then you set the volume for the occasion. However, you must realize that dB is incredibly useful for recording engineers. They are constantly balancing audio sources relative to each other, as well as the overall mix relative to the the output and the destination media (CD, radio...).

 

[earlevel]

So the 6db approximate difference between adjacent bits in a 16 or 24 bit word makes sense. so the difference between 0000 0000 0000 0001 and 0000 0000 0000 0010 would be around 6 dB. I guess my original thought was in this post that 0dB was the base reference for the threshold of hearing. As you have indicated I should have been using full scale signal as my base reference for dB. Then your numbers of around -90 and -138 for a least significant bit toggle in a 16 bit or 24 bit word respectively make some sense. So as a passing comment, the noise added by dither IS extremely small. I also read that DA converters running at 24 bit are hard pressed to reproduce analog faithfully beyond 20 bits. Not sure if that is true or relates to the delivery to the air at the end of the day.

Yes, that's a pretty good summation. On converters being hard pressed to get much beyond 20 bits:

It's a limitation of the physical world. At one end, you have the maximum output of the DAC. For argument's sake, let's say that swinging between the more negative output of the DAC (1000 0000 0000 0000 0000 0000) for two's complement) and most positive (0111 1111 1111 1111 1111 1111) yields a voltage swing of 1v (in the ballpark of consumer gear, pro will be closer to 4v). The smallest possible swing is a change in just the least significant bit, the 24th: 0...0 to 0...1. That would correspond to about 0.06 microvolts—6% of a millionth of a volt. I think you might have a sense that it's really small—to put it another way, a tenth of a millionth of the voltage level of an AA battery.

There are a lot pf places that might introduce noise that's has a higher level than that. Radio signals, 60 Hz AC power cords, noise from the power supply—you can make these as small as practical, with top components, shielding, and other design elements. But there are sources that are unavoidable, the loudest being thermal noise. Resistors simply generate noise, depending on temperature and resistance value. You have a bit of leeway on resistors used, but not enough to make it go away. And temperature can only be solved by dropping it to near absolute zero. And before you think that we can just make super-cooled DACs, that won't help you, because you'll run the DAC output to a power amp...and speakers.

But it's 100% OK, because our ears don't have that kind of range anyway. Sure, you'll see some people argue that our ears have 140 dB dynamic range, but that's not useful dynamic range. If you intend to buy a stereo capable of jet-engine maximum levels, and choose to listen at that level, then you'll take advantage of your full dynamic range capabilities. Well, for a few seconds maybe, then your ears will never again have that dynamic range.

Sorry for referencing my own stuff again, but hey, this is why they exist (be sure to read the pinned comment about referencing the full 24-bit source audio, when going past 16-bit); even with top gear, it gets pretty difficult before you even get to 20-bit: