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Bit depth / dynamic range relationship? Virtual Instrument Plugins
Old 15th August 2008
  #31
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And (again...) it's bit DEPTH (or word length). Not "bit rate" (which again, has no relation whatsoever).
Old 15th August 2008
  #32
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Quote:
Originally Posted by joerod View Post
I thought that the bits used depended upon the signal's envelope, not upon a set of increments of 6 dBs per bit...IMO, bit 1=16777216, then 1 bit + 00000001 does not equal 2 Bits (12 dBs/-132 dBFS)...Or, does it?
Nope. The full wordlength is used for every sample in linear PCM audio.

What do you mean by "12dBs/-132dBFS"? That dBs is new to me.

Quote:
The absolute output level of a 24 bit file can be greater than 144 dBs if each bit value is say, 8 dBs as opposed to 6, correct?
The absolute outputlevel (voltage) on 16bit, 24bit or any bit audio can be whatever the DAC designer decided it to be. Full output is always 0dBFS and depedning on the DAC, your speakers and amps that could be almost any SPL in the room. Dynamic range has nothing to do with playback level.

Also how can you make one bit = 8dB? And what's that "s" in dBs again? :-)

Quote:
Adding an extra bit adds 6 dB of headroom, that's why 16 bits can decode and deliver a maximum 96 dB SPL to an audio file or a CD file correct?
Depending on how you use it you can view it as headroom or footroom as mentioned. SPL does not exist in the digital domain or in the electrical analog domain, it's a measure of Sound-Pressure-Level in the air that surrounds you.

16bit give you about 96dB dynamic range from full output level down to the noisefloor but you can still play a 16bit CD at 150dB SPL if you have some serious speakers and amps. Cranking the volume this high wold definately make the noisefloor audible.

For playing back low SPL sounds in a room 24bit is overkill and 16bit is enough. It's highly dynamic material that needs more dynamic range if the noisefloor should remain low.


/Peter
Old 15th August 2008
  #33
Think of it in terms of a giant arctic squid... (I'm running out of analogies so I'm having to dig deeper here.) Consider the air speed velocity of an unladen sparrow (European of course in this instance.)
Old 15th August 2008
  #34
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Quote:
Originally Posted by Dean Roddey View Post
Think of it in terms of a giant arctic squid... (I'm running out of analogies so I'm having to dig deeper here.) Consider the air speed velocity of an unladen sparrow (European of course in this instance.)
That's even better...thumbsupheh
Old 15th August 2008
  #35
kjg
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Quote:
Originally Posted by joerod View Post

Trick question, I know. But, You CAN play a CD as high as 96 dB SPL or even higher as you said, but its headroom is always going to be -96dB.
The dynamic range is at max going to be 96 dB. and if the dynamic range of the cd is 96 dB (the max that can be represented in this medium) it's going to have zero headroom, since peaks on the cd can not go any higher without clipping.
Old 15th August 2008
  #36
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Quote:
Originally Posted by joerod View Post
With wise cracking comments like yours, I doubt anyone would want to say thanks, ever. And, even if you had good intentions, your tone seemed condescending to me. So, I won't be a paranoid if you are not a dH, deal?

I did not intend to be a smartass, rude or whatever. I don't know what a dH is and in the interest of the atmosphere in this thread I won't check it up. :-)

I think we can get along!

And yes, I know I can be relatively dry and strictly technical sometimes but we're grown ups and this IS a board for us technocrates right? We're not supposed to be very smooth with people and feelings, challenged when it comes to socail skills and all. ;-)

Also english is not my language, which at least sometimes may be a barrier.

Have a nice day Joe!


/Peter
Old 15th August 2008
  #37
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Quote:
Originally Posted by Audiop View Post
I did not intend to be a smartass, rude or whatever. I don't know what a dH is and in the interest of the atmosphere in this thread I won't check it up. :-)

I think we can get along!

And yes, I know I can be relatively dry and strictly technical sometimes but we're grown ups and this IS a board for us technocrates right? We're not supposed to be very smooth with people and feelings, challenged when it comes to socail skills and all. ;-)

Also english is not my language, which at least sometimes may be a barrier.

Have a nice day Joe!


/Peter
Communication is the way to go. I am cool with your explanation, Peter. Thanks! thumbsup
Old 15th August 2008
  #38
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Quote:
Originally Posted by Ethan Winer View Post
5) If you're reasonably good looking, become a prostitute.
Not in this economy!

Besides, there's always some young upstart willing to do it cheaper.... especially if it's unattended.
Old 15th August 2008
  #39
kjg
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Quote:
Originally Posted by joerod View Post
Dynamic range I thought, was the difference between how loud and how soft it plays...

And, what does that have to do with my playing a CD at 96 dB SPL anyway? It was just supposed to be a trick question. that's all. Maybe I didn't formulate it right.
I don't know what is so tricky about that question, but you were mixing up the terms headroom and dynamic range. There seems to be some confusion about that in these forums regularly so I felt it would be helpful to correct it. Don't get paranoid, I'm just trying to avoid confusion
You might know what you mean and just not formulate it right, but especially for less experienced people that might read these forums it is good if correct terms are used consequently.

Headroom refers to how much a signal can be raised/amplified further before before the system or medium starts distorting the signal. Like not cranking up the preamps too much while recording, allowing for peaks to be recorded cleanly and not overdrive the system on a loud passage. Or not mixing too hot on your cheap mixing board, to avoid saturating the mix buss, but rather turning up the power amps a little, so you keep headroom to accomodate peaks, and clean undistorted sound.

Dynamic range is the difference between loudest and quietest (in a piece of music, or what can be represented in a system/medium). This is expressed in dB without a reference like SPL, FS, u, m, v, V, or otherwise, which make it completely relative - just a ratio between two values.

Maybe I should have said "The dynamic range is at max going to be 96 dB because the dynamic range of the cd is 96 dB (the max that can be represented in this medium) it's going to have zero headroom (on the cd), since peaks on the cd can not go any higher without clipping."

The playback system might have more headroom though. It might for example be able to play at 106dBSPL while in your example it was playing at 96dBSPL. This means the playback system would still have 10dB headroom, before the amplifiers/speakers would start distorting.
Old 15th August 2008
  #40
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Quote:
Originally Posted by joerod View Post
Adding an extra bit adds 6 dB of headroom, that's why 16 bits can decode and deliver a maximum 96 dB SPL to an audio file or a CD file correct?
Second of all SPL is Sound Pressure Level and a playback system can be capable of greater than 96 decibels.

And first of all it is 93.3 with dither....I assume you use dither?

3rd of all, it is not "headroom".

And John Scrip is still right.

To Jay F. I thought it wasn't foot room, it was leg room? But what do I know?

Here is an article suprisingly lacking in scientific cotton candy.

Stereophile: Bits is Bits?
Old 15th August 2008
  #41
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Quote:
Originally Posted by minister View Post
To Jay F. I thought it wasn't foot room, it was leg room? But what do I know?
Well, I have big feet...
Old 15th August 2008
  #42
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Originally Posted by jayfrigo View Post
Well, I have big feet...

Please refer to Ethan's #5.
Old 15th August 2008
  #43
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And to be entirely accurate, as already alluded to in this thread, you can encode signals that are below -96 dB FS in 16 bits. It will be below the noise floor but still audible. 16 bit (or whatever) has infinite dynamic range. It just has a noise floor at around -93dB FS depending on dither type.

Alistair
Old 15th August 2008
  #44
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Quote:
Maybe a little gratefulness would be in order when people are giving of their time to help you understand these things.
FWIW, I think your explanation was great - thanks! thumbsup

I'd like to again state that bit depth, dBFS, and digital dynamic range have NOTHING to do with dBSPL in regards to maximum loudness - that is something that is controlled by the playback system. The comparisons to bit depth and dBSPL on this thread are mutually exclusive and unrelated as they have been presented.

A proper comparison would be thus: You have a 16-bit waveform that contains data that reaches Full Scale, and some that goes all the way to the noise floor of -96dBFS - let's say it's an orchestral piece with some strings that slowly decrescendo to just above 'silence.' To ensure you hear all the details, you'd have to have a playback system capable of reproducing such a large dynamic range.

Here's where it gets tricky - dBFS is only directly related to output voltage, and that can be any arbitrary amount as specified by the manufacturer of the DAC. At 0dBFS, generally the output voltage falls somewhere around +/- 10V (depends on the maximum dBu output of the gear - +22dBu is roughly 10V). Many DAC's are calibrated so that -18dBFS (correct me if I'm wrong, but I believe -18dBFS is US broadcast standard, and -20dBFS is UK standard) = 1.227V (which is 0 VU on most modern analog ballistics meters at +4dBu - some meters are nominal 0 at 0.775V), allowing for both digital and analog headroom (see kjg's post above).

So now you've got your output voltage, but how does that relate to the SPL you hear? Well, I'm a believer in Bob Katz's K- metering systems, so let's assume we want a fixed monitor gain setup where 0dBFS is equal to 99dBSPL (and therefore -14dBFS = 85dBSPL). Here's where we calibrate our system by sending a -14dBFS pink noise signal through our playback system and increase the monitor gain until our SPL meter reads 85dBSPL (it's a bit more involved than this - refer to BK's white papers and the multiple threads that have been written about this). Lock down that monitor pot, and bingo - we have a direct relationship between dBFS and dBSPL, and still plenty of dynamic range to hear your entire orchestral piece.

Hope this clears some things up!

Quote:
5) If you're reasonably good looking, become a prostitute.
HA!

Last edited by jordanstoner; 15th August 2008 at 07:44 PM.. Reason: incorrect voltages...
Old 15th August 2008
  #45
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There are a lot of weird fragmented explanations going on here, and most, if not all, has been covered, but let me try to explain it all definitively.

Firstly, let us discriminate between headroom and dynamic range. For the purposes of this post, the definitions are as follows:

Headroom - Difference between nominal signal level and highest level before distortion.

Dynamic Range - Difference between noise floor and highest allowable signal level.

Now, you can think of digital as either having no headroom or infinite headroom. This depends on your definition of "nominal signal level." I personally try to leave things at -6 to -12dbFS, thus giving myself 6 to 12dB headroom.

Let us assume, for the sake of simplicity that your system is set up to play at 144dB at 0dBFS.

A 2 bit audio signal passed through this system will play at 144dB, but the noise floor will be at 132dB, or -12dBFS. This system has 12dB of dynamic range. Similarly, a 4 bit signal will still play at 144dB, but the noise floor has now reduced to 120dB. You now have 24dB of dynamic range.

Keep in mind that you are not effectively increasing the resolution of any specific part of the dynamic range. There are no more quantization steps between -12dBFS and 0 in the 4 bit system than there were in the 2 bit system.

To continue, a 16 bit signal will still be playing at 144dB, but the quantization noise will have subsided to 48dB. Still, you are not gaining resolution, only dynamic range. And finally, your 24 bit signal will once again play at 144dB, with a noise floor at theoretical 0dB. I say theoretical, because as of right now even the best converters manage around 112dB of dynamic range at best.

So, an increase in bits, as can be seen, does not also mean an increase in possible loudness.
Old 15th August 2008
  #46
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All this talk about 96 and 144 dB dynamic range makes me a bit afraid that someone will end up with the impression that real dynamic range is something that can be explained by a single number. So let me just elaborate on 16 bit for a moment. The 96, or actually 98.089 referenced to sine, 93dB with flat dither or less with shaped dither - are numbers that does NOT tell the actual dynamic range.

Actually, the use of single numbers to describe complex phenomena as music is far from good enough to describe anything meaningful. If the 96dB range was from the measureable level of one sinewave to the other, as the idea seems to imply (to me, at least), CD format would sound more like 12 bit or so. The actual range is at the top not limited to 0dBFS, the real peaks can exceed zero if there are intersample overs. That's important but just an digression in the question of dynamic range of CD. The bottom limit can be at the last bit, the -96 number so often touted, but that is only if the signal is truncated!

With dither, dynamic range is endless. Sans for the noise dither noise floor. A sine wave can be heard about 4dB below the dither noise floor(IIRC the psychoacoustics correct), across the frequency spectra. The noise floor is not at -96 compared to the full scale sine. Noise is the same as a bunch of sines all over the spectra at once. The sum of all that energy may be -96 or -85dBFS or whatever, but it doesn't mean that the available range stops at -96 or -85dBFS. At any particular frequency, the level of the noise is quite low. Speaking of "FFT level" vs "time domain level" makes sense in the same way as RMS vs peak.

The picture below shows a -120dBFS peak sinewave in a 16 bit triangular dithered system:

(FFT is never totally accurate unless extreme precaution is taken when testing. The peak doesn't show up as -123dB RMS even though that's what it is. it doesn't correspond with what we hear either. FFT is an indication only, at best..)

Note that the dither is flat. More range at any given frequency can be had for the price of less range in other frequencies. Noise shaping can extend most of the noise floor well below the -130 bottom in the graph above, though with a bump at ultrasonic.

Speaking of dynamic range only makes sense as a technical term to describe the available range of numbers in a digital notation system, not a description of the perceivable range in an audio reproduction system.

The spread out nature of sound in the frequency spectra also explains why we don't use the top end of the FFT. We don't listen to sinewaves. The upper end of the FFT will always be left alone. People often compare FFT domain levels as indicated on THD charts in gear tests with the single/time domain numbers like 0dBFS. That have given rise to an unfortunate notion that anything measuring below 100 on the FFT is good enough. Compare that to FFT peaks of usual music in the -20 to -50 area and -100 on the FFT suddenly cuts the dynamic range to 50-80 dB.. Gimme -150 on the FFT and I'm a happy hifi camper!


Quote:
Originally Posted by 24-96 Mastering View Post
- Are we alone in the universe?
- Is there a god?
- What is the meaning on Life?
- The middle east conflict - why won't they just give it up?
- How to get rich quickly with minimal effort.
- if you want to
- if you want to
- live in present like there is no tomorrow, build for the future as if we are eternal. or something like that.
- 42
- prostitute is a good idea, in some way or the other. selling one self is part of most money making deals.


Cheers & good weekend everyone!

Andreas Nordenstam - hurrying back to work..
Old 15th August 2008
  #47
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Quote:
Originally Posted by jordanstoner View Post
Dude, get over it. Either learn how to accept criticism or stop posting silly "trick questions" that you then only "reformulate" when you've received the correct answers. Saying, "oh, that's not what I actually meant and you were wrong to correct me because you should've known what I really meant to say" only makes you look like a jackass twice, whereas apologizing for the wrong "information" (if you'd call it that) and then accepting advice gracefully will make you look like you're actually a good, stand-up guy willing to learn something rather than try to sound right all the time by covering up your mistakes - and who knows, you *might* actually learn something in the process.
Well said, and what I was thinking as well.

Quote:
Originally Posted by jordanstoner View Post
Not a bad idea. Minister, John, will you guys be at AES? Maybe we can all wear "John Scrip is still right." t-shirts.
I will, as a matter of fact. And I like the t-**** idea, though Chris Athens makes an intersting appeal for Ethan's #5. Maybe on the back of the shirt it says "Please refer to Ethan's #5". Scented perhaps? Scratch n' sniff?
Old 15th August 2008
  #48
kjg
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Quote:
Originally Posted by joerod View Post
FWIW, here is the trick question *correctly* formulated:
"Adding an extra bit reduces the noise floor by 6 dB, while a 16 bit CD can deliver over 96 dB SPL, correct?"
No, a cd cannot deliver 96dB SPL. A speaker could. The SPL addition means you are now linking the dB (which is in itself just a ratio) to an absolute reference, in this case a reference of sound pressure level.
The cd (or any medium) has as dynamic range, which is expressed as the difference (ratio) between the noise floor and the highest value that can be expressed without distortion. How loud that would be (in dB SPL) or what voltage that would result when the cd is playing sample value y in dBV or dBu, depends on how powerful the amps and speakers are and or how the DAC is calibrated.

The dB itself is a ratio, not an absolute quantity. Only when linked to a given reference (whether it is voltage, sound pressure level, or other wise) it expresses an absolute value.

The difference between two quantities in dB (the ratio between the two quantities) is by definition calculated as follows:

Difference in dB = 10 * log10 (quantity 2/quantity1)

So, if you have 10 bananas and I just 1, you have 10 * log10(10/1) = 10dB more bananas than I do. Or, the ratio between the two quantities of banana is 10dB.
If you have 100 bananas and I 10, you still have 10dB more bananas than I, because it is a relative unit expressing a logarithmic ratio. You see how it is still ten times as much? That is why. 20dB more than 1 would be a factor 100, 30 dB more a factor 1000, etc.

Say I would now define a new dB reference, the dBBanana.
The reference quantity will be 0.1 bananas.

If I tell you I measured 20 dBBanana in my fruit bowl today you can calculate how many bananas are in my fruit bowl using the inverted formula 10^x/10 = (quantity 2/quantity1) as follows:

"^" denotes "to the power of".

10^20/10 = number of bananas in my fruit bowl/reference quantity

10^20/10 = 10^2 = 100 so:

100 = number of bananas/0.1 so:

number of bananas = 100 * 0.1 = 10

So now you know I have 10 bananas in my fruit bowl. Pretty useful, huh? You can express a ratio, or an absolute value if you link the dB to a reference.

Quote:
Originally Posted by joerod View Post
Happy now?

Make a T-Shirt, then sell it to GS users...
I agree with what others have already stated: You should be grateful that people are actually taking time to explain something to you, and/or correct your erroneous and confusing statements.
I don't need your gratitude though, because the only reason I am not ignoring you is because I don't want other, nice and smart people to be confused by you.
How confused you are about dBs (or anything else for that matter), I really couldn't care less. Simply because I find you a rude person with an inflated ego.
I know you always want to have the last word, no matter how much ignorance or rudeness you already have displayed since you registered on this forums, so give it your best shot.

Have a nice day

PS: I got hungry typing this so I'll go have 2 bananas now. Care to calculate what the remaining dBBanana level in my fruit bowl will be?

PS2: The term bit rate refers to an amount of bits per time unit (transfer speed). Since pictures do not develop in time (as opposed to an audio of video stream), the term bit rate does not apply to your picture example.
You meant to say bit depth. If you know it all, why don't you use the correct terms? And why don't you thank John Scrip for correcting you instead of being rude?
Old 15th August 2008
  #49
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Quote:
Originally Posted by Dean Roddey View Post
... Consider the air speed velocity of an unladen sparrow (European of course in this instance.)
What is your favorite colour?
Old 16th August 2008
  #50
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Perhaps driving in the fog is a better analogy. A fog with 16 meters of visual range will allow you to perceive less detail at 15 meters than a fog with 24 meters visual range. However thick the fog is you are still going to damage your car when you hit someone who crossed the street without looking and couldn't here you because the hip hop music on there ipod was too damn loud.
Old 16th August 2008
  #51
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I want to thank Ethan for having the best answer in this thread.

I want to thank Lupo for being cool about a badly formulated question and still made an effort to explain in a polite manner.

I want to also apologize to all the Slutz. My badly formulated trick question was not meant to troll or derail anything, the intention was to challenge users to expand on answers. Sorry, it didn't come out the right way....
Old 16th August 2008
  #52
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Quote:
Originally Posted by joerod View Post
I want to thank Ethan for having the best answer in this thread.
Thanks, but which answer do you mean? The one explaining 6 dB per bit, or that prostitution is a great way to make a lot of money quickly?

heh

--Ethan
Old 16th August 2008
  #53
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Quote:
Originally Posted by Ethan Winer View Post
Thanks, but which answer do you mean? The one explaining 6 dB per bit, or that prostitution is a great way to make a lot of money quickly?

heh

--Ethan
If it wasn't obvious then I am sorry. Yes, 6 dB per bit.
Ethan, I only make fun of those who asked for it...
Old 16th August 2008
  #54
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Riccardo, I really think you are making the wrong call here. At the very least you missed post #35, #45, #53, #56 and #57 but frankly, I think you should remove the trouble maker instead of deleting the responses. This will keep going on as long as he is here...

Alistair
Old 16th August 2008
  #55
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Quote:
Originally Posted by UnderTow View Post
Riccardo, I really think you are making the wrong call here. At the very least you missed post #35, #45, #53, #56 and #57 but frankly, I think you should remove the trouble maker instead of deleting the responses. This will keep going on as long as he is here...

Alistair
Hi Alistair, hope you won't mind if I quote you to generally address everybody around here and convey or rather re-enforce the message.

Should it not be clear already, the matter here is about "feeding" ..... well before we move on to other "matters"

I am sure you'll understand.

There are things that are (and have been for a long time) not tolerated like "confrontation", "personal calling out" , "bickering" or the frequent " I am better than you 2 year old childish thingy" or even worse " I can cut a better master than you", as well as the unexpected "minding someone else's business and associated practices" and so on.

These rules common amongst human beings gifted with intellect have been blatantly and at every occasion ignored.

Not by a single party though.

Ignoring the person or the people that upset you is much better than ignoring the rules.

That would help the mods in doing their job.
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