[jaud]

 
Quote:

It seems to me that there is a lot of misunderstanding regarding what bit depth is and how it works in digital audio. This misunderstanding exists not only in the consumer and audiophile worlds but also in some education establishments and even some professionals. This misunderstanding comes from supposition of how digital audio works rather than how it actually works. It's easy to see in a photograph the difference between a low bit depth image and one with a higher bit depth, so it's logical to suppose that higher bit depths in audio also means better quality. This supposition is further enforced by the fact that the term 'resolution' is often applied to bit depth and obviously more resolution means higher quality. So 24bit is Hi-Rez audio and 24bit contains more data, therefore higher resolution and better quality. All completely logical supposition but I'm afraid this supposition is not entirely in line with the actual facts of how digital audio works. I'll try to explain:

When recording, an Analogue to Digital Converter (ADC) reads the incoming analogue waveform and measures it so many times a second (1*). In the case of CD there are 44,100 measurements made per second (the sampling frequency). These measurements are stored in the digital domain in the form of computer bits. The more bits we use, the more accurately we can measure the analogue waveform. This is because each bit can only store two values (0 or 1), to get more values we do the same with bits as we do in normal counting. IE. Once we get to 9, we have to add another column (the tens column) and we can keep adding columns add infinitum for 100s, 1000s, 10000s, etc. The exact same is true for bits but because we only have two values per bit (rather than 10) we need more columns, each column (or additional bit) doubles the number of values we have available. IE. 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 .... If these numbers appear a little familiar it is because all computer technology is based on bits so these numbers crop up all over the place. In the case of 16bit we have roughly 65,000 different values available. The problem is that an analogue waveform is constantly varying. No matter how many times a second we measure the waveform or how many bits we use to store the measurement, there are always going to be errors. These errors in quantifying the value of a constantly changing waveform are called quantization errors. Quantization errors are bad, they cause distortion in the waveform when we convert back to analogue and listen to it.

So far so good, what I've said until now would agree with the supposition of how digital audio works. I seem to have agreed that more bits = higher resolution. True, however, where the facts start to diverge from the supposition is in understanding the result of this higher resolution. Going back to what I said above, each time we increase the bit depth by one bit, we double the number of values we have available (EG. 4bit = 16 values, 5bit = 32 values). If we double the number of values, we halve the amount of quantization errors. Still with me? Because now we come to the whole nub of the matter. There is in fact a perfect solution to quantization errors which completely (100%) eliminates quantization distortion, the process is called 'Dither' and is built into every ADC on the market.

Dither: Essentially during the conversion process a very small amount of white noise is added to the signal, this has the effect of completely randomizing the quantization errors. Randomization in digital audio, once converted back to analogue is heard as pure white (un-correlated) noise. The result is that we have an absolutely perfect measurement of the waveform (2*) plus some noise. In other words, by dithering, all the measurement errors have been converted to noise. (3*).

Hopefully you're still with me, because we can now go on to precisely what happens with bit depth. Going back to the above, when we add a 'bit' of data we double the number of values available and therefore halve the number of quantization errors. If we halve the number of quantization errors, the result (after dithering) is a perfect waveform with halve the amount of noise. To phrase this using audio terminology, each extra bit of data moves the noise floor down by 6dB (half). We can turn this around and say that each bit of data provides 6dB of dynamic range (*4). Therefore 16bit x 6db = 96dB. This 96dB figure defines the dynamic range of CD. (24bit x 6dB = 144dB).

So, 24bit does add more 'resolution' compared to 16bit but this added resolution doesn't mean higher quality, it just means we can encode a larger dynamic range. This is the misunderstanding made by many. There are no extra magical properties, nothing which the science does not understand or cannot measure. The only difference between 16bit and 24bit is 48dB of dynamic range (8bits x 6dB = 48dB) and nothing else. This is not a question for interpretation or opinion, it is the provable, undisputed logical mathematics which underpins the very existence of digital audio.

So, can you actually hear any benefits of the larger (48dB) dynamic range offered by 24bit? Unfortunately, no you can't. The entire dynamic range of some types of music is sometimes less than 12dB. The recordings with the largest dynamic range tend to be symphony orchestra recordings but even these virtually never have a dynamic range greater than about 60dB. All of these are well inside the 96dB range of the humble CD. What is more, modern dithering techniques (see 3 below), perceptually enhance the dynamic range of CD by moving the quantization noise out of the frequency band where our hearing is most sensitive. This gives a perceivable dynamic range for CD up to 120dB (150dB in certain frequency bands).

You have to realize that when playing back a CD, the amplifier is usually set so that the quietest sounds on the CD can just be heard above the noise floor of the listening environment (sitting room or cans). So if the average noise floor for a sitting room is say 50dB (or 30dB for cans) then the dynamic range of the CD starts at this point and is capable of 96dB (at least) above the room noise floor. If the full dynamic range of a CD was actually used (on top of the noise floor), the home listener (if they had the equipment) would almost certainly cause themselves severe pain and permanent hearing damage. If this is the case with CD, what about 24bit Hi-Rez. If we were to use the full dynamic range of 24bit and a listener had the equipment to reproduce it all, there is a fair chance, depending on age and general health, that the listener would die instantly. The most fit would probably just go into coma for a few weeks and wake up totally deaf. I'm not joking or exaggerating here, think about it, 144dB + say 50dB for the room's noise floor. But 180dB is the figure often quoted for sound pressure levels powerful enough to kill and some people have been killed by 160dB. However, this is unlikely to happen in the real world as no DACs on the market can output the 144dB dynamic range of 24bit (so they are not true 24bit converters), almost no one has a speaker system capable of 144dB dynamic range and as said before, around 60dB is the most dynamic range you will find on a commercial recording.

So, if you accept the facts, why does 24bit audio even exist, what's the point of it? There are some useful application for 24bit when recording and mixing music. In fact, when mixing it's pretty much the norm now to use 48bit resolution. The reason it's useful is due to summing artefact's, multiple processing in series and mainly headroom. In other words, 24bit is very useful when recording and mixing but pointless for playback. Remember, even a recording with 60dB dynamic range is only using 10bits of data, the other 6bits on a CD are just noise. So, the difference in the real world between 16bit and 24bit is an extra 8bits of noise.

I know that some people are going to say this is all rubbish, and that “I can easily hear the difference between a 16bit commercial recording and a 24bit Hi-Rez version”. Unfortunately, you can't, it's not that you don't have the equipment or the ears, it is not humanly possible in theory or in practice under any conditions!! Not unless you can tell the difference between white noise and white noise that is well below the noise floor of your listening environment!! If you play a 24bit recording and then the same recording in 16bit and notice a difference, it is either because something has been 'done' to the 16bit recording, some inappropriate processing used or you are hearing a difference because you expect a difference.

G

1 = Actually these days the process of AD conversion is a little more complex, using oversampling (very high sampling frequencies) and only a handful of bits. Later in the conversion process this initial sampling is 'decimated' back to the required bit depth and sample rate.

2 = The concept of the perfect measurement or of recreating a waveform perfectly may seem like marketing hype. However, in this case it is not. It is in fact the fundamental tenet of the Nyquist-Shannon Sampling Theorem on which the very existence and invention of digital audio is based. From WIKI: “In essence the theorem shows that an analog signal that has been sampled can be perfectly reconstructed from the samples”. I know there will be some who will disagree with this idea, unfortunately, disagreement is NOT an option. This theorem hasn't been invented to explain how digital audio works, it's the other way around. Digital Audio was invented from the theorem, if you don't believe the theorem then you can't believe in digital audio either!!

3 = In actual fact these days there are a number of different types of dither used during the creation of a music product. Most are still based on the original TPDFs (triangular probability density function) but some are a little more 'intelligent' and re-distribute the resulting noise to less noticeable areas of the hearing spectrum. This is called noise-shaped dither.

4 = Dynamic range, is the range of volume between the noise floor and the maximum volume.

I don't know if this has be said before (didn't want to read through all 50 odd pages of replies) but that's not entirely correct. The basic principles are correct, but the aspects of audio quality are not. 
 
Let me explain, as we increase the bit depth we not only increase the dynamic range (which in my opinion is like a cherry on top) but we do increase the accuracy of the audio. It goes a little like this; as stated above the sample rate (measure in Hz) is the amount of times per second that the analog audio is indexed (or sampled) each sample 'remembers' (or expresses) only one thing, its amplitude which is expressed in a digital word ie binary. So a in CDDA (Compact Disc Digital Audio) we sample at 44.1kHz and we use a 16bit word length (or bit depth), each sample has a 16bit word telling the digital system what amplitude it is and weather it is positive or negative phase. What the samples are effectively doing is drawing a graph of the analog signal, just as you would join the dots to create a picture in a kids book. Are you with me so far? Alright, with a 16bit word length we can express ~65,000 different values, which means we express ~65,000 different levels of amplitude. I hear you ask, but what happens if the analog signal falls between one of the these ~65,000 values? Well, that's where 24bit world length come in, it can express over 16 million different levels of amplitude. 
 
So as you can see as we increase the bit depth of the audio we increase the dynamic range but we also increase the accuracy of the digital waveform, if we increase the sample rate as well we also improve the accuracy of the digital audio; remember the sample rate is how many times the analog signal is being indexed, so if we increase the sample rate we get more 'snapshots' of the analog audio waveform. Oh, and another thing studios don't record in 48bit (I don't think that 48bit actually exists in a piece of hardware) most will record in 24bit and some will record in 32bit.
 
Here's a pretty picture to illustrate what I'm talking about in regards to increasing the sample rate:
 

 
And here's another pretty picture demonstrating an increase in the bit depth:
 

 
Sources:
Studied Sound Engineering at RMIT, Melbourne, Australia
First image source: RMIT course content
Second image source: http://www.echoaudio.com/Digital%20101.htm

 

[Griffinhart]

Quote:

Alright, with a 16bit word length we can express ~65,000 different values, which means we express ~65,000 different levels of amplitude. I hear you ask, but what happens if the analog signal falls between one of the these ~65,000 values? Well, that's where 24bit world length come in, it can express over 16 million different levels of amplitude.

Specifically: 65536 and 16777216, respectively.
 
32-bit gets you 4294967296 values.
 
-- Griffinhart

 

[emmodad]

@ jaud:  in the 50+ pages of this (often technically-misinformative) thread, there have been numerous posts addressing the OP's misunderstanding (and sadly, stubborn defensiveness) wrt relationships between resolution, dynamic range, quantization error etc.  this is not the only thread on head-fi in which the OP - apparently lacking some fundamental technical understanding - has seemingly aggregated and referenced information from a variety of sources, but smoothly presents declarative conclusions of "fact" which are actually flawed; at minimum misrepresentative; or worse, false.
 
This has been the case in posts from the OP regarding digital audio theory, digital signal processing fundamentals, audio engineering, and linear systems theory, to name only a few areas.  The OP has also previously eventually admitted that they understand neither the mathematics underlying digital audio theory, nor digital audio converter design.
 
if you understand digital signal processing theory, you really should lean back with a good bottle of red wine and plow through this entire thread.  Makes for entertaining, and sometimes toe-curling, reading.
 
chuck

 

[jaud]

@chuck
I was planing on doing so but didn't have time at the time of posting, just wanted to clarify some finer details, and again sorry if im rehashing what has been previously stated in the thread, but i often find on HI-FI etc forums that most peoples knowledge on digital audio is sourced from lots of different places of varying quality. I find that most people get confused by the delicate interplay of sample rate and bit depth and what that means in terms of audio accuracy. When explain clearly (I hope that my post was clear and easy to understand, but if anyone wants some clarification or maybe some expansion please PM me or reply to this thread and I'll do my best to help 

 ) PCM digital audio is actually a very elegant and simple system for audio reproduction, I'm still trying to wrap my head around how DSD audio works though 

 
cheers,
jaud

 

[xnor]

jaud, an 8 bit signal will be output just as smooth as a 64 bit signal. The only thing that changes is the noise level assuming dither was used => dynamic range.
 
What you describe as accuracy doesn't work the way you think it does. Otherwise you'd understand DSD.

 

[stv014]

Quote:

And here's another pretty picture demonstrating an increase in the bit depth:
 

 
Although the OP does have some errors, it is correct that the "stair step" distortion on your picture is a common source of misconception, and it can be entirely eliminated by dithering (at the expense of some noise floor, hence the limited dynamic range). Here is what a dithered -90.3 dBFS sine wave looks like in 16 bit PCM format, and the result of removing the noise from the quantized signal with a comb filter. There should be no "steps" in the output of the DAC:

This is not the same as quantizing first, and then adding the noise to "mask" the distortion, as the following picture shows:

 
Quote:

 
The 48 kHz signal may look very different here, but that is because most of the energy of the analog input is in the ultrasonic range. So, what is removed is neither audible, nor typically present in music in large amounts. The audible frequency range is the same in all cases.
 

 

[D. Lundberg]

Quote:

What the samples are effectively doing is drawing a graph of the analog signal, just as you would join the dots to create a picture in a kids book. Are you with me so far?

Huh? Waveforms are not reconstructed by drawing straight lines between samples. Where did you get that idea?
 
Quote:

Alright, with a 16bit word length we can express ~65,000 different values, which means we express ~65,000 different levels of amplitude. I hear you ask, but what happens if the analog signal falls between one of the these ~65,000 values?

It will get quantized (rounded) to the closest value. The errors from quantization will (in a properly dithered system) represent noise at a level determined by the word length.
 
Quote:

So as you can see as we increase the bit depth of the audio we increase the dynamic range but we also increase the accuracy of the digital waveform, if we increase the sample rate as well we also improve the accuracy of the digital audio; remember the sample rate is how many times the analog signal is being indexed, so if we increase the sample rate we get more 'snapshots' of the analog audio waveform.

The bit depth is the accuracy (of quantization) and that accuracy determines the dynamic range and SNR.
The sample rate determines the bandwidth, so a higher sample rate means you can represent higher frequencies.

 

[jaud]

 
Quote:

Huh? Waveforms are not reconstructed by drawing straight lines between samples. Where did you get that idea?
 
It will get quantized (rounded) to the closest value. The errors from quantization will (in a properly dithered system) represent noise at a level determined by the word length.
The bit depth is the accuracy (of quantization) and that accuracy determines the dynamic range and SNR.
The sample rate determines the bandwidth, so a higher sample rate means you can represent higher frequencies.

No waveforms are not reconstructed by drawing strait lines between samples, I'm using that as an example to illustrate what samples in PCM digital audio are doing, hence the use of the word "effectively", i feel that by using this example (and I've found that most people understand that when I say this I'm not talking literally but figuratively) that it is easier to understand role sample rate plays in PCM audio. Let  me put it another way, "samples only remember two things, their amplitude and their phase, each sample is effectively taking a snap shot of the analog signal at a certain point in time, then when played back in the same window of time a group of samples will 'render' a version of the analog signal"
 
Yes, the value will get quantized if it fall between level of amplitude that can be captured by the digital system, but that is not a true representation of the amplitude.
 
That's true, but with more (to use a similar wording as my example above) sample per second we gain more "snapshots" of the analog signal and can there for 'track' or 'render' more minute changes in the amplitude of the analog signal, pair that with a higher bit depth (which means we can record many more different levels of amplitude, with less distortion of the original analog signal when using quantization)

 

[jaud]

 
Quote:

 
Although the OP does have some errors, it is correct that the "stair step" distortion on your picture is a common source of misconception, and it can be entirely eliminated by dithering (at the expense of some noise floor, hence the limited dynamic range). Here is what a dithered -90.3 dBFS sine wave looks like in 16 bit PCM format, and the result of removing the noise from the quantized signal with a comb filter. There should be no "steps" in the output of the DAC:

This is not the same as quantizing first, and then adding the noise to "mask" the distortion, as the following picture shows:

 
 
The 48 kHz signal may look very different here, but that is because most of the energy of the analog input is in the ultrasonic range. So, what is removed is neither audible, nor typically present in music in large amounts. The audible frequency range is the same in all cases.
 

Yes, the stair step distortion picture isn't' the best example, but what it does show is the raw uncorrected performance improvements which can be obtained by recording and consequently reproducing PCM digital audio at higher bit depths.
 
Also the images that you have used are working on a completely different time scale, with the lack of a scale indication, I would presume that these images represent a sine wave over a much long period of time than the image that i used, which I would presume was is a representation at a much smaller time frame, I emphasise the use of the word presume.
 
 
 

 

[D. Lundberg]

Quote:

Originally Posted by jaud /img/forum/go_quote.gif
No waveforms are not reconstructed by drawing strait lines between samples, I'm using that as an example to illustrate what samples in PCM digital audio are doing, hence the use of the word "effectively", i feel that by using this example (and I've found that most people understand that when I say this I'm not talking literally but figuratively) that it is easier to understand role sample rate plays in PCM audio. Let  me put it another way, "samples only remember two things, their amplitude and their phase, each sample is effectively taking a snap shot of the analog signal at a certain point in time, then when played back in the same window of time a group of samples will 'render' a version of the analog signal"

Alright, but the kids book analogy is a bit misleading since those books are about drawing straight lines between points and not about summing sinc-pulses (that would be a strange book

) like digital audio.
If you want people to understand digital audio you'll need to stop using that example and focus on explaining Nyquist/Shannon and Fourier.
 
Quote:

Yes, the value will get quantized if it fall between level of amplitude that can be captured by the digital system, but that is not a true representation of the amplitude.

It is a true representation of the amplitude, and it will be accurately represented whether you use 2 or 32 bit quantization. That's the beauty of the Nyquist theorem (and dither).
The difference is in the amount of background noise you'll get and consequently the dynamic range.
 
How do you think DSD or delta/sigma-converters would work if you couldn't get the correct amplitude using just a few bits?
 
Here is a real example to show you that it actually works:
 
A sinewave, 1kHz @ -0.9dB, 24 bit.

 
Now what happens to the sinewave if you reduce the bit depth to 8 bit?
You'll get the same 1kHz @ -0.9dB sinewave with the addition of quite a bit of background noise (from quantization):
 

 
Quote:

That's true, but with more (to use a similar wording as my example above) sample per second we gain more "snapshots" of the analog signal and can there for 'track' or 'render' more minute changes in the amplitude of the analog signal, pair that with a higher bit depth (which means we can record many more different levels of amplitude, with less distortion of the original analog signal when using quantization)

A waveform has four basic characteristics: frequency, amplitude, phase (relative to other waveforms) and dynamic range.
If the sample rate is more than twice as fast as the highest frequency the signal contains, then you'll know three of those. The bit depth will give you the fourth one: the dynamic range.
 
The real limits imposed by the sample rate and bit depth are in bandwidth and dynamic range. If the signal is within those constrains it can (if the implementation allows it) be accurately represented and reconstructed.

 

[estreeter]

I view this thread along the same lines as I view similar debates on jitter, and it largely comes down to this:
 
- what would it cost me to buy the 'optimum' solution ?
 
- assuming I could afford said solution, would these old ears even benefit from all that technology ?
 
No, I'm not a Luddite and I dont have cloth ears, but I do realise how skilful many DAC makers are in the time-honored technique of baffling us with BS. I know Head-Fi is a 'bigger is automatically better' cave, but if something sounds good to me at 24/96 (or, gasp, 16/44.1 ...), I'm not going to spend 2K on a DAC simply because the numbers excite the tech geeks among us. 

 

[jaud]

 
Quote:

I view this thread along the same lines as I view similar debates on jitter, and it largely comes down to this:
 
- what would it cost me to buy the 'optimum' solution ?
 
- assuming I could afford said solution, would these old ears even benefit from all that technology ?
 
No, I'm not a Luddite and I don't have cloth ears, but I do realize how skillful many DAC makers are in the time-honored technique of baffling us with BS. I know Head-Fi is a 'bigger is automatically better' cave, but if something sounds good to me at 24/96 (or, gasp, 16/44.1 ...), I'm not going to spend 2K on a DAC simply because the numbers excite the tech geeks among us. 

Although my previous posts in this thread probably dint show it, but when I am researching and demoing gear etc. this for me is the ultimate decider on the purchase because i feel that the pursuit of Hi-Fi and audiophilia is the pursuit of gain pleasure form recorded music, not the pleasure of know that you have the best or most expensive gear/rig 

 
 

 

[estreeter]

I would add the fascination many Head-Fiers have with asynchronous USB DACs over any other implementation, regardless of the reputation many of the older DACs had prior to Gordon Rankin sat down to write his asynch code. If it works, fantastic, but getting hung up on buzzwords for their own sake is just crazy, IMO. 

 

[khaos974]

@jaud: An interesting experiment to show that bit depth translates into noise level (which is another way to say dynamic range) rather than accuracy, here is a 4-bit file with dither, and you should notice that the fact that it's 4 bit isn't really heard as inaccuraccy but a very high noise level.
 
And before someone asks, it shows up as an 8-bit file, but it really is 4-bit, the samples only take 16 values, 0, 16, 32, 48, 64..., none of the intermediate values are used.
 
Download Extract.zip - 5.9 Mb
 
PS: I cheated a little, some of the noise is far outside the audible range.

 

[milosz]

Stairstep waves?
 
If you were listening to a signal recorded in the four least significant bits of a 16 bit recording, it would be VERY low in level; probably inaudible. My listening room has a noise floor about 70 dB below my max listening level.  4 LSB's would be a signal at -72 dB.  This is below the noise floor of my listening room, so really if sounds recorded at 4 bit levels are full of artifact, well, I will barely be able to hear the fundamental of a sound that is below my ambient noise level, and those harmonics caused by the artifact will be at least 6 dB below THAT- geez, you know, I'm just not going to worry about artifacts that are nearly 10 dB below the sound of my computer fan in the other room.
 
I mean- just think about it.  If you have adjusted your listening level to be pretty LOUD- that would be 100 dB peak levels. These artifacts induced by low-bit-levels are going to most be right at or well below your ambient noise floor.  (OK, if you are listening at ROCK CONCERT levels of 115 dB or higher, your ears are shot anyway and you're not going to be able to hear most of this high-end super-fi hi-rez stuff.)
 
See http://www.engineeringtoolbox.com/nc-noise-criterion-d_725.html  background noise levels in residential settings are 30~45 dBA, so if you are listening at 100 dBA the signal-to-noise level is 55 dB to 70 dB.   Now tell me a signal at -80 dB with artifact harmonics 10 dB below THAT is going to really matter (the - 90 dB unwanted harmonics would be 10 dBA if you are listening at 100 dBA, or AT LEAST 20 dB BELOW THE NOISE FLOOR OF A VERY QUIET HOME)
 
OK, so let's forget about recordings of music using the 4 LSB. Let's talk about real recordings, where we are someplace between maximum (0 dB) and maybe 60 dB down.
 
After the signal comes out of the DAC process it is indeed "jumping" from one level to another instead of a smooth transition.  But now this "jaggy" signal train goes into a LOW PASS FILTER and part of this filter's job is performing integration over a specified timescale, factored by appropriately chosen coefficients- so when the signal comes out of the filter, those "jaggy" artifacts should mostly be gone, and if the sampling frequency is sufficiently high to allow employing a low pass filter that allows the entire audible spectrum to pass through, well, we have a smooth waveform as long as we started with a fair number of bits to begin with. Most of the content in recorded music is using at least 8~10 of the available 16 bits, and after the low pass filter you're really not going to have much 'stairstep' artifact in there, the percentage of stairstep will be a ratio of least-significant-bit to number of bits in the signal, so for all but the quietest passages the artifact is way down there in % terms.  
 
When we try to record a sine wave using just the LSB or maybe the two least significant bits, we are more likely to see quite some amount of artifact in the output of the "brickwall" filter, but the signal is  will be ~90 dB down (2 bits out of 16  anyway so a little extra harmonic content resulting from this artifact-laden waveform is going to be present, but that harmonic content will be lower than the level of the fundamental, those unwanted harmonics will be something like -100 dB I'd guestimate (ref to 0 dB, not ref to the fundamental)- so, even though a 24 bit signal has much less artifact in it's -90 dB presentation of waveforms, can you really HEAR that?  I mean, 90 dB down from full level is certainly well at least 20 dB below the level of ambient noise in my home- and unless you live in an anechoic chamber, it probably is in yours, too. 
 
( AN ASIDE: People are always talking about how great analog sounds in comparison to digital, because there's no digital artifact-  but if you can show me a vinyl system that actually has even a 60 dB s/n ratio from the ACTUAL LP SURFACE -not just the electronic s/n ratio of the phono stage- - well, I'd be impressed.  My own measurements show me that most LPs are lucky to offer 50 dB of actual s/n ratio.  Tape  can be a little better, but unless you are listening to a master tape.... well we could go on here but let's not.)
 
So, yeah, a 24 bit recording is going to have measurably less artifact at very low levels. But at actual music recording levels? Gee, not so much. And at actual in-room listening levels?  Not much at all, almost none.
 
And while all this engineering analysis is useful, we're in fact talking about human perception here, not just noise levels and harmonic power analysis. And when it comes to humans using their ears to judge sound, I don't think there has been ANY A/B/X study showing that anyone- from golden eared audiophiles to musicians to regular folks- who can reliably tell what is 24/96 and what is 16/44.1.  You could probably devise some kind of test tone that might make the difference apparent, but on music signals [size=10pt]I don't believe anyone has been found that can beat chance. [/size][size=10pt]Of course, just because no positive results for A/B/X 24 vs 16 bit identification testing has does not PROVE that no one can really hear the difference- you have to test EVERY HUMAN BEING to make that claim.  However, if a large sample of people including those with advanced training in terms of critical listening skills such as musicians and audiophiles has been shown to be unable to pick the hi-rez file in a blind test, I for one am willing to say that's "close enough for practical purposes" and will take it to mean that in all probability I can't hear the difference.  And that's all that matters to me-  I'm the one who buys gear and recorded music for me, and if I can't hear the difference between redbook and 24/96 recordings, well then I see no need for me to spend my hard-earned cash on exotic DACs or hard-to-find 24/96 recordings. [/size]