16 bit vs 24 bit vs 35 bit vs 36 bit vs 64 bit DAC sampling


I have limited knowledge about DAC's, but as I understand it, a typical CD player used to have 16 bit sampling, and supposedly no one was supposed to be able to hear the difference between anything more than 16 bit sampling; however, I recently purchased an Esoteric K-01X, which has 35 bit sampling (why 35 bits? no doubt only to differentiate it from their then top of the line 36 bit sampled Grandioso series).  

Now I can hear a big difference between my old Musical Fidelity kW DM25 DAC with 24 bit sampling (circa 2005), and the newer Esoteric DAC with 35 bit sampling, although I'm not supposed to, although maybe there are some other electrical programs playing with the sound besides the sampling rate.  

Now, there are 64 bit sampling DAC's, and I'm wondering how much the ear actually does hear from the sampling, or if it's something else entirely that's making the digital sound better?  

Any insightful opinions or perspectives?  

Thanks.
drbond

An audiophile friend gave me a book for Christmas, written by Robert Harley, "The Complete Guide to High-End Audio".  The quote below, which explains what I hear quite adeptly, is from that book, pg 231, from the section titled, :"16 Bits, 20Bits, 24 Bits":

"...the benefits of the increase in word length from 16 to 18, 20, and even 24 bits are not in dispute.  As I mentioned earlier, word length is the number of bits used to encode the audio signal's amplitude at each sample. Assigning a number--called a word--to represent the audio signal's amplitude is called quantization.  The word length determines the system's resolution, dynamic range, distortion, and signal/noise ratio.  We also call the word length resolution. . .

....the greater the number of bits in each digital word, the more precisely the analog signal's amplitude is encoded. . . The longer the quantization word, the more steps, and thus the finer the resolution.  

. . . .the resolution of a digital audio signal isn't defined by the maximum number of bits available, but the by the number of bits being used at any given moment.  

The advent of 20- and 24-bit digital audio not only expands the dynamic range, but also increases the resolution of low-level detail.  This low-level detail can be fine nuances of an instrument's timbre, which enhance the sense of realism.  It can also be subtle spatial cues, such as discrete  acoustic reflections and reverberation decay, which the ear interprets as a more convincing reprodution of the original recording venue. 

Longer word lengths also contribute to better sound because the postproduction (mixing, equalization, signal processing) common in the recording or mastering studio can be performed with much greater mathematical precision.  Moreover, any noise added by these processes is spread out over a wider bandwidth, which makes it less audible.

The combination of higher sampling rate and longer word length results in greatly improved sound quality.  (A digital system's resolution can also be increased by adding to the signal a small amount of noise, called dither...)"

He then proceeds to outline the limitations of 20+bit processing, often calling the additional bits, simply marketing bits, fi they're not done right, and that for most systems any information over 20 bits is "rarely capable of delivering real audio information"

So, I needless to say, it appears simple, but it quickly becomes a complex issue. 

Larry - i think you understand the difference but could be confusing others/readers.  120 dBSPL is not the same as having a SNR of 120 dB.  You can listen at 80 dB and have the noise floor at essentially zero.  But, as i believe you assume, for there to be any benefit to a 120 dB SNR we'd need to listen at 120 dB above (1 million times0 the ambient noise in undisturbed air (whatever that is).
So yea, its clear that these numbers are mostly irrelevant which is why i posted the few practical reasons for bit depth > 16 (or 18 if you really want to push the boundaries of hearing).
The valid reasons have to do with mixing & truncation for various needs; and IMO are not beneficial in the end product.
I doubt if anyone without a jug if moonshine could hear the difference between the levels of bit rate or sampling rates! Damage risk for an 8 hr time period is 85dBSPL- who is sitting through 120dBSPL!
before the game of bit and sampling is managed ?it would be nice is if companies would standardize measurements and present amp and speaker specs so a decent matching can be realized!
most of the terms thrown around are not fully understood nor are the parameters of the human hearing mechanism in its “normal “ or “abnormal “ status.
Many audio buffs have hearing loss either due to age, illness or trauma; these too complicate the listening experience!


to several who have noted (correctly) that 20 bits is all that can be truly used ( and I'd argue more like 17), but wonder, "why 32, 35, 64, (finger to mouth 1 million)?
Before going on i have also seen "but rate" and "but depth" used.   Let's be clear: its bit depth, although that impacts bit rate. Yet in lossless transmission, its not even close to linear since most of those bits are zero.  Basically is 2 to the Nth power dynamic range. 16 bits means 2^16th ~ 96,000:1. 24 bits means 16.7Million:1. 

Some good and bad reasons.
  1. marketing. But i honestly think this is not as central as maybe imaged by the cynics
  2. More bits - say 24 gives huge benefits in the studio.  levels sets can be off.  Mixing can be done and when you lose a but or two, its not big deal.
  3. With enough bits, we can perform  volume control and DSP int he digital domain with minimal if any losses - and all the math truncations are below the level of audibility.  I personally think this is a huge advantage especially going forward since we cna right many wrongs without all the processing distortion we suffer today.


Remember that the analog processing before the digital rendition does not have infinite signal to noise,and remember that a DAC is an analog chip, subject to noise and distortion.  Even 24 bits is WAY beyond this threshold.
G
The actual true limit in bits is 20 for digital , the recast are extra bits that fillin a guesstimate , there are plenty of high tech white papers from Mojoaudio , Schiit Audio that explain in-depth 
dontget caught up in  that it’s engineering  quality makes much more of a difference and dac type many prefer the older Multibit 
Dac chip , which-are a form of a R2R  but on one  big chip 
and werel laser trimmed , like Burr Brown 1704, or Analog devises 1955, for example. Tom dacs have 2-3 linear power supplies 
and excellent filtering and pre and post regulation , noise is jitter 
and the better dacs have all this and a bunch of other parts in the engineered design , but it isnot cheap, also many quality dacs 
are now starting to implement a seperate streamer module 
that is also filtered and has linear power supplies.
high quality cost $$.

on the topic of bit depth used in recording nad mastering, there are many reasons why more than 16 bits are used.  And, today, almost ALL recording and mastering is done at 24 bits. Must be better for us right?
No.
reason #1 is so that if levels are off ( remember 0vU levels sets?) there is sufficient headroom to keep all 16 bits int he end product.  You can record too high and not clip, or too low and not lose bits on the low end.

#2 is so that in the inevitable (regrettable too) mixing, processing etc. the fidelity lost is below the least significant of the 16 bits. I won get into how digital level math is done but if you think about it it may become clear that you have both Least common denominator (speaking loosely) issues and truncation issues.

So it allows for sloppy production.  OK, tha's harsh, btu not too far off.  It also allows for multi-track mix-down. Yuk again, but reality especially in rock/grunge/pop/hip-hop/rap.

Want to hear what properly level-set and unmixed 16 bits can do? Listen to old Verve or Mercury Living Presence.  Old 3 channel analog recordings. Careful levels sets. Loving attention to detail. Minimal processing. Superb.  16 bits
Nyquist goes to Hz sampling (the vertical aspect in the time domain) and the step landings - horizontal bits - would become narrower with higher Hz sampling rate.
This is a bit confusingly worded. Harry Nyquist inferred from Shannon’s work (its basically a corollary) that sampling at **higher than** 2X the highest frequency allows the original waveform to be reconstructed perfectly. yes it is the X coordinate of what becomes a Cartesian graph, when viewed as PAM. (pulse amplitude modulation).

The caveats are:
  1. higher than, not = 2X. At precisely 2X you can get the wrong answer. Its called an alias.  For example a 1 kHz 1V sine wave sampled at precisely 2X could land samples all at zero (silence) all at 1V (perfect recreation), all at 0.5V (off by half) or anywhere in the middle.

  2. perfect reconstruction. Not in this world.

  3. ...but we can get very close. Likely much closer than a) analog does (maybe 60-70 dB on a good day) and also b) likely distortion below the levels of our hearing

  4. another issue is that one ought not measure distortions as "all created equal". Music theory tells us that, if pleasure is the desired result, this is not so. Dissonance and consonance are pretty well understood.

  5. In the end arguing for "perfection" misses the point that no system is perfect, and vinyl is a long way from perfect, as is tape.


1. timing/jitter (read the blog at sonogy research.com).
2. noise on the ground of digital signals, that either pollutes the analog ground or impacts jitter (back to #1)
3. Filtering - the reconstruction part, both by shifting the frequencies so they are easier to filter (that's what over sampling or up sampling essentially achieves) or building better filters.  A filter can bee deep, or linear, but typically not both. So the bit I wrote about "only after the reconstruction filter" means these filters can be imperfect.  Can be?  Are.  I'll also point out that that @cleeds said "its math".  True enough, but there is an ocean of difference between theoretical math, and practical implementations. Analog is perfect in theory too.

4. part B of the filters is that there are some very small signals that need to be amplified or impedance transformed at the output of a DAC.  Both present good old analog amp challenges, not all that different from a moving coil cartridge.
5. never underestimate the impact of regular old audio blocking and tackling.  Power supplies. Amps.  grounding.  parts selection.  Do you know how many DACs depend on relatively pedestrian chip opamps and ok-but-not-awesome power supplies?  Most.  You know why?  Its easy and cheap compared to doing it from scratch.
@itsjustme 

What do you perceive as the greatest challenges and areas for digital to excel?

Thanks. 
There are no "stair steps" in digital audio.
Correct, but only after reconstruction filtering.

For people who want to learn about it, you really ought to go back to the original journal articles by the pioneers in telecom int he 1960s - from the Bell Labs Technical Journal and the Lenkurt Demodulator, the Demodulator being very accessible and written for the client base, not researchers.

Slowly a set of blogs on this and related topics is appearing on Sonogy Research's blog as well.


Digital has several challenges. IMNSHO, bit depth is not at the front of the line.


My opinion is that you like the new DAC but it has little to do with bit depth. Others have noted that you are limited by the original recording anyway.  Its the weak link theory (kinda like life).

I'll also point out that many of my absolute favorite recordings are in fact analog tape originals, digitally mastered to Phillips Red Book (16/44.1), but lovingly with proper levels set, filtering, etc.  The devil, as always is in the details.  Using Michelangelo's brush will not allow me to paint the Sistine Chapel.
noske
I understand the steps appearance in the time domain. Instead of the sinewave looking smooth in the time domain, it looks stepped up in increments, then down, up, down with the flow of the sinewave ... As bit rate increases, the size of these steps decrease. With 65,536 of the little buggers, I reckon the curve would be pretty smooth(but not continuous) ...
No, you’re mistaken. That’s why I provided you a link that demonstrates it for you visually. There are no "stair steps" in digital audio.
In any event, I query the theorem that a continuous signal may be obtained. One may be approached.
Do you understand the difference between a theorem and a theory? Do you understand that a theorem is a fact proven by math? That you don’t understand or accept the math, or that you won’t watch a video to learn, doesn’t invalidate the theorem.

Digital audio is not intuitive. It’s math.
Hello,
I don’t think you would ever need above 22 bit even though the come as 24 bit. The rest you are hearing is the awesome Esoteric. The rest of the stuff in that box is awesome. You should hook up a $29 Walmart DVD player and hear how good it sounds. 
The bitrate is set by the source in this case I assume you're referring to red book CD which is 16/44.1 . The CD player  upsamples to 35 bit, what comes out the analog end is not 35 bit you're lucky if it's 16 . Any difference you hear between various players is in the way they upsample and reconstruct.  
@cleeds

I understand the steps appearance in the time domain.

Instead of the sinewave looking smooth in the time domain, it looks stepped up in increments, then down, up, down with the flow of the sinewave. The horizontal aspect.

As bit rate increases, the size of these steps decrease. With 65,536 of the little buggers, I reckon the curve would be pretty smooth (but not continuous), in the scheme of tings.

Nyquist goes to Hz sampling (the vertical aspect in the time domain) and the step landings - horizontal bits - would become narrower with higher Hz sampling rate.

In any event, I query the theorem that a continuous signal may be obtained. One may be approached.

I don’t click on links.
I thought my point was about bitrate, in that Audio note are only 16bit and they are developing a 12bit, and suggesting to check out Peter Qvortrup's views on bitrates, but heyho!
Maybe the bitrate and sample rate have nothing to do with sound quality.What maters is the DAC's ability to create music form a signal its given.
@alan60 

I hope this doesn't turn into a "this is better" or "that is better" thread, but I have listened to a high end dCS SACD player in my system before I purchased the Esoteric, and it sounded much worse than my 15 year old Musical Fidelity player for the type of music that I listen to (purely acoustic classical); however, the dCS were much better for rock n' roll bass response.  

Nevertheless, please try to contribute to the subject matter of bit sampling effect on DAC/CD playback.  

Thanks. 

Everyone has a opinion ,Peter at Audionote is far from a expert 
on digital he is far from a digital engineer.
i know AN well I lived in the U.K for over 10 years 
tubes have their own bloom ,Aqua Lascala for example I feel better balanced hybrid are great ,Lampi too has their Tube fans 
With Mosfets and Multibit dac chipsets you can get a lot of the tube goodness ,without the tube artifacts , that’s why we all have 
choices. 

You should check out Peter Qvortrup of Audio Note UK's views on higher bitrates, he is talking about bringing out a 12bit player. I am a vinyl man, but the higher end Audio Note Cd players and DAC's are the most Musically engaging digital format I have heard, and that includes top DCS gear, Kondo/CEC, etc.
@audioman58

Your recommended article seems to explain much about the discussion. The article does immediate clarify one thing that I have noticed: older late 1950’s recordings sound much quieter and clearer on the Esoteric with the much higher bit sampling than it did on the Musical Fidelity with the 24 bit sampling.

Here is the summary from one part:

"So why on Earth would they even create a digital recording format that can’t even be listened to?!?!?!?!?

Simple: bit-depths and sampling rates far above the range of human hearing are used during the recording, editing, mixing, and mastering processes to lower digital noise in audible spectrum when recordings are downsampled to the significantly lower resolution sold in commercially released recordings."


...so, during the down-sampling process of the signal in the DAC, that 35 bit analysis is making some recordings sound much better. . .

However, in the same article, the discussion about the power supply is quite interesting, and how a very quiet power supply would be needed to sample above 20 bits. . .
clearthinker
... the wave form of digital sampling is a jagged zig-zag saw, like an endless flight of stairs. The little triangles at created by joining the teeth of the saw is a measure of the departure of the digital representation from the true waveform of the sound ...
It’s amazing that this misnomer still exists two decades into the third millennium. Digital audio may have its problems, but "stairsteps" ain’t it.

We know from Nyquist that we can get a continuous (analog) signal from a digitally discrete code provided that the bandwidth is half (or less) of the sampling rate. This isn’t a theory - it’s a theorem. It’s a fact.
The higher the sampling rate the smaller the little triangles and the closer you get to the original sound.
Not so. The higher the sampling rate the greater the bandwidth.

For those who can’t comprehend this truth, this video may help.
One of the best things Audio Classics did for my mx110z was remove the 55 year old corroded rca jacks and replace them with new gold plated jack panels.

I also changed to locking RCA connectors (both ends).

Every time you change a piece of equipment, you break/make fresh connections with the interconnects, AND, moving one cable may rub up against another, causing it to move at it's connection point.

Ah, magnifico!


For me I heard the biggest improvement over bog standard 16 bit when I went to an upsampling DAC that could do 20 bit, when recordings that were either recorded or remastered at higher bit rates than 16.  I've owned subsequent DACs where the upsampling could be disabled and I've fooled around a little trying to determine how much the upsampling mattered and with standard 16 bit discs it makes a difference, but on better recorded fare, not so much.  I don't even know why my current DACs are capable of because once they go over 20 bit it doesn't seem to matter.
Yes 16 bits is plenty I agree.

But the sampling rate is much more important.
As every high school math graduate knows, the wave form of digital sampling is a jagged zig-zag saw, like an endless flight of stairs.  The little triangles at created by joining the teeth of the saw is a measure of the departure of the digital representation from the true waveform of the sound or, rather, the music you want to listen to.

The higher the sampling rate the smaller the little triangles and the closer you get to the original sound.

Of course, if you want the original sound, you have to listen in analogue.


I use a Pioneer  CD player (PD-F1009) which is s a 1 bit DLC machine, circa 2000 and rolls 300 + 1 cds all day long. Granted this is in an outdoor system for background music by the pool but everyone loves the sound.  Could it be better? Sure, but for me why go there $$$$.
That you hear a ’big difference’ may stem from the fact that the analog circuitry behind the two DAC's is different, or that the digital audio processor uses some kind of filtering or effects to create a certain ’sound profile’.

There’s no difference to the human ear between 16 bit sampling or more bits, since the only change is the dynamic range / noise floor. The other parameter is sampling frequency ... higher frequencies can reproduce more higher harmonics of instruments, but since most people can’t hear much above 16kHz there’s not much sense in that either.

Higher rates are used in studios for mixing purposes, where signals are being treated in the digital domain with filters and effects like reverb, phasing, tube sims, limiters, compressors and what have you.

It can even be hard to hear a difference between uncompressed and compressed digital audio. Do this test to determine if you can hear the difference:

https://www.npr.org/sections/therecord/2015/06/02/411473508/how-well-can-you-hear-audio-quality
What does it sound like? If the new DAC is better does it matter how they got there? I have several DACs, do they sound the same, definitely not. 
They do some processing at higher bitrates. If they have a digital volume control it is better to start with 32 bits than 24 since they will basically throw away bits later.

Other processing than volume is possible and there it is also better to start with more bits.

For sampling frequency it is usually the filtering you want to improve. They need to have filters and the filters affect the sound quality. If they start with 96kHz the filter hopefully only affects a part of the spectrum we can't hear.

There are articles about this If you google. For everyone saying that you can't improve the signal from what was as input that is actually wrong. You may make it worse but you can calculate more samples in a way that it probably improves the sound for most music. You just need math and a very fast processor. The Chord MScaler does this if I am not mistaken. 
"attaining outstanding powers of expression" - good Latinate pomposity.
+1. That's marketing, not engineering.
The Esoteric ad copy is classic.
"In excess of 32 bits," immediately specified to 35 bits.
"fully 2,048 times resolution" because 2**(35-24) = 2048. The "fully" is laughable; do other vendors stop at 2000 times?
"attaining outstanding powers of expression" - good Latinate pomposity.

Whatever you're hearing, it's not the bit depth.  If indeed you have a 35 bit DAC, which I doubt (regardless of manufacturers claims), I guarantee the bottom 20 bits are lost in the room noise.
Read this about digital 20 true bits is all that is currently possible 
Ben at Mojo Audio knows his digital and builds a very good dac .
https://www.mojo-audio.com/blog/the-24bit-delusion/
@audioman58 

If 20 bits is all that is possible, why are the engineers chasing the bit rate higher to 64 bit rate now?  I suppose there's alot of people who don't understand what they are doing with the bit rate?  Maybe this is this akin to selling the $4,000 XLR cable when the $60 cable is as accurate as you'll get. . . 

So it's the other features of the unit that make it sound so much better?  I suppose it's the transport, the power supply, the more accurate clock, the high slew rate, large current, and digital filters that are playing the larger role of improving the sound quality.   

Here is the ad from the Esoteric K-01X features page:

35 bit D/A Processing

The K-01X combines multiple 32-bit DAC chipsets and utilizes 35-bit D/A processing algorithm to convert the PCM signal to analog at a high resolution in excess of 32 bits. 35-bit processing achieves an astounding resolution that is fully 2,048 times that of 24-bit processing. In the digital range, full advantage is taken of high-bit data gradation to minimize calculation errors and provide faithful conversion to analog, thereby attaining outstanding powers of expression with even extremely small music signals.


20 actual bits in digital is all that is possible ,with  turntables 12.5 bits Schiit audio Mike Moffett 
has extensive knowledge base,over 25 years, on digital and what is actually possible ,and all other bits are  estimated in reading ,it gets very technically involved ,but very much worth the read.

@jasonbourne52  
Yeah buddy. 120 dB SNR is indeed overdrive. Especially when streaming services never beat 60.  
competently designed DACs today have way less than .1 percent harmonic and intermodulation (IM) distortion! You want some "coloration"? Add a tube output stage!


Then why do a lot of these dacs  with great measurements sound etched and give me a headache, doesn't sound very accurate to me.
@djones51: All competently designed DACs today have way less than .1 percent harmonic and intermodulation (IM) distortion! You want some "coloration"? Add a tube output stage!
Having a 35 bit depth DAC is like using an atomic clock for an egg timer. Your increase in sound quality is probably a compilation of lots of things including the transport and the power supply.
"So, most of the markedly improved sound that I hear is from the improved transport stability, and more precise laser reading, and not from the 35 bit samplin"

I would say a large portion of the sound quality improvement could most definitely be attributed to the higher precision operation and higher quality built standard. I believe that some have a tendency to grossly under estimate the necessity of a good CD transport . They are a vital component if you favor Redbook CD usage.
Charles 
@djones51

So, most of the markedly improved sound that I hear is from the improved transport stability, and more precise laser reading, and not from the 35 bit sampling?  There must be some other software aspect to the improved sound as well. . .
DACs are components I never worry about anymore I just use the one in my preamp. As long as you're talking about competently built DACs which can give a good 16 -18 bits they are not anything that can be heard unless they have been designed with a sonic signature.
@jasonbourne52

Well, around the same time I plugged in my new Esoteric K-01X and started playing it, with 35 bit sampling, a rabid bat did attack a man in my county!
@drbond : Wrong! There is NO smoothing of digital "steps"! The reconstructed waveform is presented complete! Increasing the sampling frequency does nothing to make waveforms below 22 kHz more "analog" like! Read my above post.
The sampling rates they are talking about is only within the DAC . It's not what comes out on the analog end you're lucky to get as much as 20 bit depth, the best I've seen is the new Topping D90se which does 22 bit distortion free.
The sample rate is just how many times per second an electrical measurement is taken. It is expressed in HZ (cycles per second). 44.1 kHz was chosen for the CD Redbook standard because it enables full encoding for a 22 kHz musical waveform. This is at or beyond human hearing. Higher sample rates are only good for bats and dolphins!
I believe the higher bit rates make it easier to perform the conversion pushing noise and distortion beyond human hearing, it also improves digital volume control if at least 32 bit is used. 
@jasonbourne52

The manufacturers seem to indicate in their literature that the bit sampling is how much the digital steps from the signal are smoothened to sound more analog.  
All these higher bit rates are just oneupmanship to confound the unwary and sell product!
A DAC can only output whatever the original recording bit rate was. It cannot increase the source's bit rate! You would have to listen at 120 db to hear the noise floor of a 16 bit recording - if you didn't go deaf in 10 minutes!