School me on analogue to digital conversion.

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Sammas

Well-known member
Joined
Sep 30, 2004
Messages
547
Location
Sydney, Australia.
I understand the usual... Bit depth = amplitude. Sample rage = frequency. Nyquist's theorem. Truncation, dither and word length. The reason quantisation noise is always half the value of the least significant bit, which subsequently is why 1bit = 6dB of dynamic range... despite the fact that a lot of people take it literally as in 1 bit is actually designated to a certain 6dB of dynamic range.

One thing that baffles me is, the notion that 16bit converters use only 14bits and that 24bit converters use only 21bits, etc. Within computer science, the word length and resolution remains constant. IE: 0000 0011 or 0111 0011 are two eight bit values. Within PCM audio, both exist as a positive peak signal. The former is closer to . The latter is quite close to 0dbFS clipping.

This question is sparked by an interview with Daniel Weiss that I read: http://blog.georgenecola.com/interview-daniel-weiss/

I found this comment interesting: If I use my RME converters for 24 bit/44.1 kHz conversion, what sort of converter module is involved? Is it a 5 bit module that does 64 times oversampling?

Could be. One really cannot tell in general. In the past there were 1 bit Delta/Sigma converters, which did 64 times or 128 times oversampling. These were sampled down with appropriate noise-shaping. “24 bit” only tells us the amplitude of the word length at the converter output. This says nothing of the quality of the conversion. Some read 24 bit and think that it is TRULY 24 bits! This is not the case. Very good converters do well to have 20 bits of resolution!


Why is it?

 
The manufacturer tag line tells you the transport bit depth, but nothing about the signal to noise ratio.

Think of a 16 seater bus. It can hold up to 16 people, but most public transport buses are 50% empty. Those empty seats are noise, the populated seats are signal.

A 16bit converter will never be able to drive more than 96dB, due to its interface. 24bit is the next logical step (as we like to work in 8's). Theoretically, it could drive 144dB of dynamic range, but at there is no converter technology (think of the analog side) that can support that.

Now, many have shown that a lower noise floor can be created using dither, but that's a post for my laptop, not tapping away on my iPhone :)
 
JohnRoberts said:
Why is what...?

JR

Why are 24bit converters limited to 21bits of real world resolution... and 16bit converters to 14bit, etc.


Rochey said:
The manufacturer tag line tells you the transport bit depth, but nothing about the signal to noise ratio.

Think of a 16 seater bus. It can hold up to 16 people, but most public transport buses are 50% empty. Those empty seats are noise, the populated seats are signal.

A 16bit converter will never be able to drive more than 96dB, due to its interface. 24bit is the next logical step (as we like to work in 8's). Theoretically, it could drive 144dB of dynamic range, but at there is no converter technology (think of the analog side) that can support that.

Now, many have shown that a lower noise floor can be created using dither, but that's a post for my laptop, not tapping away on my iPhone :)

Hey Rochey, I was hoping you chimed in.  :)

I understand the real world challenges of noise floor... but in my head it doesn't translate to reduced resolution (IE: only using 21 bits of 24).

A positive peak signal (0dBFS) in 24 bit is 0111 1111 1111 1111 1111 1111, in which no bit represents any value anywhere near the real world -115dB noise floor of modern converters. Its a peak at 0dbFS.

If it were converted to a base 10 example, an 0dBFS peak is equal to 8,388,608. Its like saying that the last few digits are "noise"... when the noise only exists below 300,000.

Where am I going wrong?


 
Sammas said:
JohnRoberts said:
Why is what...?

JR

Why are 24bit converters limited to 21bits of real world resolution... and 16bit converters to 14bit, etc.
They are limited by practical circuit implementation.  The input is an analog signal that must get sliced and diced by analog circuitry during the conversion steps. Even a simple comparator the heart of every conversion, has analog noise and linearity criteria. 

While I suspect a modern 16 bit convertor could deliver very close to it's theoretical limit 24 bit convertors are still challenged by reality. 
Rochey said:
The manufacturer tag line tells you the transport bit depth, but nothing about the signal to noise ratio.

Think of a 16 seater bus. It can hold up to 16 people, but most public transport buses are 50% empty. Those empty seats are noise, the populated seats are signal.

A 16bit converter will never be able to drive more than 96dB, due to its interface. 24bit is the next logical step (as we like to work in 8's). Theoretically, it could drive 144dB of dynamic range, but at there is no converter technology (think of the analog side) that can support that.

Now, many have shown that a lower noise floor can be created using dither, but that's a post for my laptop, not tapping away on my iPhone :)

Hey Rochey, I was hoping you chimed in.  :)

I understand the real world challenges of noise floor... but in my head it doesn't translate to reduced resolution (IE: only using 21 bits of 24).

A positive peak signal (0dBFS) in 24 bit is 0111 1111 1111 1111 1111 1111, in which no bit represents any value anywhere near the real world -115dB noise floor of modern converters. Its a peak at 0dbFS.

If it were converted to a base 10 example, an 0dBFS peak is equal to 8,388,608. Its like saying that the last few digits are "noise"... when the noise only exists below 300,000.

Where am I going wrong?
It's complicated, even more now with advanced oversampling convertors that convert higher sampling rate, less bit depth samples down to more bits at lower sample rates. In this process the noise gets re-arranged to.

It is instructive, at least it was for me, to study the data sheets for popular convertors. The better data sheets will provide "analog like" data to help make sense of modern conversion performance. We can't just look at any one metric (like number of bits) and extrapolate analog performance at all levels from that. I find it useful to look at noise and distortion (linearity) separately and at different signal levels.

JR
 
Sammas said:
Why are 24bit converters limited to 21bits of real world resolution... and 16bit converters to 14bit, etc.

"In the world of digital audio, overloads are not musically interesting — they are horrid, unmusical and unpleasant things that really must be avoided. Since digital systems can not record audio of greater amplitude than the maximum quantising level, engineers decided to define the digital signal reference point as this maximum. The top of the digital meter scale is thus 0dBFS, FS standing for 'full scale'.

As on analogue systems, it makes sense to build in some form of operational headroom to cater for the odd loud peak. This, however, is where all the confusion and problems occur. Since analogue equipment typically provides 18dB or more of headroom, it seems sensible to configure digital systems in the same way. After a little trial and error the Americans adopted a standard of setting the nominal analogue level (+4dBu) to equate with -16dBFS in the digital system, thereby accommodating peaks of up to +20dBu (ie. 0dBu equals -20dBFS). In Europe we have standardised on 0dBu equating to -18dBFS, thereby tolerating peaks of up to +18dBu.

This artificially created headroom provides a reasonable degree of protection against transient overloads, but will generally mean that the average level of material recorded into a digital system will be down around -12dBFS. This is not a problem as far as the quality of the recording is concerned — particularly if you are working with a 20- or 24-bit format — since the noise floor will still be at least 84dB below the nominal programme level, a figure which is far better than that achieved by any analogue recording system. In effect, operating in this way simply configures the digital system to have similar characteristics and performance to an analogue one."

from
http://www.soundonsound.com/sos/may00/articles/digital.htm

-12dBfs equals 2 bits loss.

Regards,
Milan
 
moamps said:
"In the world of digital audio, overloads are not musically interesting — they are horrid, unmusical and unpleasant things that really must be avoided. Since digital systems can not record audio of greater amplitude than the maximum quantising level, engineers decided to define the digital signal reference point as this maximum. The top of the digital meter scale is thus 0dBFS, FS standing for 'full scale'.

As on analogue systems, it makes sense to build in some form of operational headroom to cater for the odd loud peak. This, however, is where all the confusion and problems occur. Since analogue equipment typically provides 18dB or more of headroom, it seems sensible to configure digital systems in the same way. After a little trial and error the Americans adopted a standard of setting the nominal analogue level (+4dBu) to equate with -16dBFS in the digital system, thereby accommodating peaks of up to +20dBu (ie. 0dBu equals -20dBFS). In Europe we have standardised on 0dBu equating to -18dBFS, thereby tolerating peaks of up to +18dBu.

This artificially created headroom provides a reasonable degree of protection against transient overloads, but will generally mean that the average level of material recorded into a digital system will be down around -12dBFS. This is not a problem as far as the quality of the recording is concerned — particularly if you are working with a 20- or 24-bit format — since the noise floor will still be at least 84dB below the nominal programme level, a figure which is far better than that achieved by any analogue recording system. In effect, operating in this way simply configures the digital system to have similar characteristics and performance to an analogue one."

from
http://www.soundonsound.com/sos/may00/articles/digital.htm

-12dBfs equals 2 bits loss.

Regards,
Milan

That article is sorta correct in that a wise designer sets a "nominal operating level" (say, -18 dBFS) to allow for headroom, but then again, the wise analog designer also sets a "nominal operating level" (say, 0 dBu) to allow for headroom. The analog voltage rails are a hard limit on the absolute peak level of a signal in the circuit and this is no different from 0 dBFS.

-a
 
Andy Peters said:
No. Word length (where did this "bit depth" thing start?) defines the dynamic range and thus the theoretical noise floor.
Don't know...  :-[ mea culpa

I think the majority of confusion comes from the number of bits (is that ok?) relationship to theoretical performance. As we often experience theoretical and practical are two different things.

Watch this video. All will be clear.

-a
+1, good vid

JR
 
Andy Peters said:
Sammas said:
I understand the usual... Bit depth = amplitude.

No. Word length (where did this "bit depth" thing start?) defines the dynamic range and thus the theoretical noise floor.

Watch this video. All will be clear.

-a

No, technically word length relates first and foremost to the quantisation of amplitude. The video even covers it. At the most basic level, word length correlates the number of input values that share the same output value. The smaller the word length, the more input values that share the same output  value, the greater the quantisation error in mapping amplitude.

Quantisation error is always defined as half the value of the least significant bit. For the simple reason that if a value is smaller than the size of the least significant bit, it has only two values it can be. 0 or 1.

Increased word length = increase in the accuracy of amplitude = decrease in error that manifests as the noise floor.

Essentially the only way the theoretical noise floor can lower, is if amplitude is mapped with less error.

My exact point of confusion is that everyone is using the noise floor as a point of reference, despite the fact that the accuracy of the waveform throughout the entire dynamic range contains less error overall. I can understand that this isn't an issue upon straight reproduction of audio (IE: CD)... but in most modern studios where is a lot of stuff that happens on a mathematical and data level before any waveform is even reconstructed.
 
There are 16bit converters that offer the 16bits worth of SNR. TI's PCM270x Usb Converters are an example where the device is mostly limited by the interface, not by the actual DAC inside the part. (and no, don't ask me if we'll do 24bit versions...)

I liked your decimal conversion concept... and you nailed the description too "everything below 300,000 is noise", however, I like to think of it a few decimal points over... everything below 0.0000xyz is noise. :) We're talking about the least significant bits. bits that are usually drowned by the large level signals.

On a 24 bit converter, those last few bits are so low in voltage that most system designers worry about the thermal noise from large value resistors. That's how teeny tiny they are! :)

finally, just to throw some mud in in the air... did you know that with some averaging of data, it's possible to "see" the 25th bit of data in a 32bit data stream on the PCM1795? why do we care about the 25th bit of data? Why do we care about 32bit datastreams?
Because many systems do their volume control in the digital domain, and push data further and further into the LSB's.
Because most audio DSP's are 32bit these days, pushing a 32bit audio sample in a 32bit register, down a 32bit pipe is nice and easy!
Because Marketing guys need jobs.

;)
 
I've seen that video a few times.  If there is only one unique solution for a lollipop plot, why do converters *sound* different?  Why is the ProTools interface several thousand dollars, and the Apogee MiC only a hundred or so?  Why does my Symphony I/O sound so much more 3D compared to my MOTU Traveler? 
 
mulletchuck said:
I've seen that video a few times.  If there is only one unique solution for a lollipop plot, why do converters *sound* different?  Why is the ProTools interface several thousand dollars, and the Apogee MiC only a hundred or so?  Why does my Symphony I/O sound so much more 3D compared to my MOTU Traveler?

Because there are people willing to spend more money for them.  8)

No one says that every X bit digital path is identical. Like i said earlier in this thread look at the analog specs when available. There are filters involved in the conversion back to analog.

If two digital paths sound dramatically different at least one is wrong, maybe both, but digital technology these days is very good.

JR
 
mulletchuck said:
I've seen that video a few times.  If there is only one unique solution for a lollipop plot, why do converters *sound* different?

Because the analog circuitry varies from product to product?
Because the clocking varies from product to product?
Because the modulators in the converters vary from chip to chip?

  Why is the ProTools interface several thousand dollars, and the Apogee MiC only a hundred or so?

Channel count? DSP capability in the hardware?

Why does my Symphony I/O sound so much more 3D compared to my MOTU Traveler?

Analog circuitry around the converters? Power supply design? Clocking?

-a
 
Sammas said:
No, technically word length relates first and foremost to the quantisation of amplitude. The video even covers it. At the most basic level, word length correlates the number of input values that share the same output value. The smaller the word length, the more input values that share the same output  value, the greater the quantisation error in mapping amplitude.

Quantisation error is always defined as half the value of the least significant bit. For the simple reason that if a value is smaller than the size of the least significant bit, it has only two values it can be. 0 or 1.

Increased word length = increase in the accuracy of amplitude = decrease in error that manifests as the noise floor.

Essentially the only way the theoretical noise floor can lower, is if amplitude is mapped with less error.

Sorry to dredge up an old thread, but a very important aspect of sampling and noise has been overlooked.

The amplitude resolution of a sampled signal (i.e. the number of bits) does determine the resolution of the channel and thus its noise floor - essentially, the noise power of the sampler. However, if this noise power is spread over a wider frequency range by sampling the signal faster, then the noise power _density_ will decrease, and so the total noise over a fixed bandwidth will be lower, even though the quantizer has the same resolution (number of bits).

It's best to think about noise as a density, sort of like a gas. Zoom in on it in the frequency domain, and it gets smaller and smaller. Aggregate a wider frequency range and it builds up. In any sampled system, there is a fixed amount of quantization error that has to be distributed from -Fs/2 to Fs/2, i.e. over the frequency band bounded by half of the sample rate. Increase the sample rate, and the density over a fixed bandwidth can decrease.

This is how one can make a 2 or 3 bit converter operating at a few MHz that has a very low noise floor over a 22.05KHz bandwidth - the required quantization error is spread out over a very wide band, and that can be filtered away when the signal is resampled to a far lower sample rate.

So, to get back to the original assertions, yes, the 'number of bits' of a linear PCM sampler does impose an absolute lower bound on the error of sampling. However, this error is distributed within the bandwidth of the sampler, with the only requirement that the sum over this bandwidth is equal to the 'required' error power. By using a higher sampling frequency, the error is spread to frequencies that are out of the desired frequency band, thus reducing the amount of error in the desired passband. Getting even fancier, it's possible to move this error disproportionally to out of band frequencies, further increasing the resolution in the desired frequency band. This is what 'oversampling' is all about, and why sigma-delta converters can use only a bit or two and result in well over 100dB of resolution.

Regards,
 
Sammas said:
JohnRoberts said:
Why is what...?

JR

Why are 24bit converters limited to 21bits of real world resolution... and 16bit converters to 14bit, etc.
As Rochey noted the real world and physics limits the dynamic range of practical convertors to less than the theoretical 144 dB

I suspect a 16b convertor "could" deliver full 96 dB dynamic range, but I doubt they do. I am not aware of any physical limit, but more a consideration for how the noise floor sounds. When customers perform the WFO test feeding a tiny few LSB sine wave into it. With a pure digital noise floor the sine wave gets severely distorted by the LSB quantization. If instead the bottom bit (or bits) are dithered by noise. That same low bit sinewave is much less distorted while mixed with the noise. A trade off between LSB noise or LSB quantization distortion. Noise sounds better than distortion .

As digital gets better we have to revert to good old analog specs to characterize them (a good thing IMO), but they will never be completely apples to apples, but getting close enough for government work.
Rochey said:
The manufacturer tag line tells you the transport bit depth, but nothing about the signal to noise ratio.

Think of a 16 seater bus. It can hold up to 16 people, but most public transport buses are 50% empty. Those empty seats are noise, the populated seats are signal.

A 16bit converter will never be able to drive more than 96dB, due to its interface. 24bit is the next logical step (as we like to work in 8's). Theoretically, it could drive 144dB of dynamic range, but at there is no converter technology (think of the analog side) that can support that.

Now, many have shown that a lower noise floor can be created using dither, but that's a post for my laptop, not tapping away on my iPhone :)

Hey Rochey, I was hoping you chimed in.  :)

I understand the real world challenges of noise floor... but in my head it doesn't translate to reduced resolution (IE: only using 21 bits of 24).

A positive peak signal (0dBFS) in 24 bit is 0111 1111 1111 1111 1111 1111, in which no bit represents any value anywhere near the real world -115dB noise floor of modern converters. Its a peak at 0dbFS.

If it were converted to a base 10 example, an 0dBFS peak is equal to 8,388,608. Its like saying that the last few digits are "noise"... when the noise only exists below 300,000.

Where am I going wrong?
There are lots of white papers on the subject of modern conversion and they can explain this better than I. Noise is a complex entity that must be considered in terms of it's amplitude and bandwidth. Some of the modern convertors shift the spectral energy of noise outside the audible band. I need to stop before I say something really wrong. Short answer it is not simple linear relationship when digital filtering gets involved in the post processing of conversions.

Thinking of digital conversions in strictly theoretical terms is not productive (unless you use the advanced theories around oversampling and decimation et al.). Google is your friend.

JR
 
JohnRoberts said:
Thinking of digital conversions in strictly theoretical terms is not productive (unless you use the advanced theories around oversampling and decimation et al.). Google is your friend.
Actually Stan Lipsh*tz & John Vanderkooy are your true friends in this.  :)

Usually when the Dynamic Duo produce a paper on any subject, there is nothing more to be said.  However, they saw fit to release more than 1/2 a dozen papers on this topic  :eek:

I suspect a 16b convertor "could" deliver full 96 dB dynamic range
The 20k Hz bandwidth noise of a properly dithered (with TPDF noise, the most efficient 'simple' dither) is -93.32dB down from a FS sine wave.

This would be a 'perfect' 16b convertor.

There are certainly devices which have textbook 16b 44.1 & 48 kHz performance.

eg the old IBM T2x & T4x laptops.  Alas, only a few expensive MACs have anything as good today.

The first good 16b convertor I encountered was the Sony PCM-F1.  You can take a sine wave 20dB BELOW the noise floor and still hear a clean, if very noisy, sine.  It's even better trying this with piano music and is a good test of any digital transmission chain as it exercises loadsa stuff that people don't realise are important for good sound.

On the other hand, there are many 24b soundcards & recorders with less practical dynamic range than a good Dolby cassette recorder.  These are those that don't quote an analogue spec.  But zillion bits & MHz gotta be better innit?  ;D
 
Funny to see Stanley Lipshitz's name altered by the profanity auto correct. 

It's his actual name.    8) If searching his papers in google put the 'i' back in...

JR
 

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