mix-paste, mix-paste invert

Some might recall from my first post in this thread that I see the residue in Spectral View and on the Frequency Analysis graph. The Statistical Analysis just puts certain numbers on it.

Somebody correct me if I'm wrong, but I don't recall any version of CEP having Spectral View. 
Having said that, I'm going to scrape off the residue of this thread and let Andy chase his tail without my participation.

pwhodges and 2Bdecided are correct, except for the full scale thing.  I can reproduce the situation in Audition 1.5. 
It has nothing to do with CE2K or 16.8, which is exactly equivalent in precision to 0.24 and 24.0:  they all maintain
24 bits of precision (16+8 = 0+24 = 24+0).  It is not a bug, but a limitation of the floating point format.

There's nothing special or lossless about 24-bit precision in a floating point format.  What if it were only a 4-bit precision
floating-point format?  Would you expect worse precision?  Then, what about 48-bit precision?  Better?  There is
always a potential for loss when combining floating point values, it's just that at 24-bit, we're safe from hearing these
losses in normal listening circumstances.

To explain what is happening, imagine for simplicity a 12-bit floating point format with 4 bits of precision instead of 24, and two
values to be added.  Number A is 15 and the Number B is 2.  That's 1111 ( 8+4+2+1 ) * 2^0 and 1000 ( 8 ) * 2^-2 (other bits in
the 12 (or 32)-bit number contain the power of 2).  These numbers are normalized so that the first
bit is always a 1, and therefore assumed, but not actually represented in the data, so we represent only the last 3 bits of
precision (111 for 15 and 000 for 2).  We add the two numbers which, with infinite precision equals 17.  That's 10001 (1*16 +
0*8 + 0*4 + 0*2 + 1*1).  Normalized, the 12-bit floating point format with 4 bits of precision representation has the first bit as 1,
leaving 3 bits of representation left: (1)000 = 16, not 17.  There are not enough bits to represent 17.  There is loss!

In your 32-bit precision floating point with 24 bits of precision example, the loss registers as -168 dB or whatever.  It would takes
lots and lots of operations for these losses to be heard (for the error to creep up from the 24-bit level to say, the 13-bit level. 
The person editing the audio need not be concerned, but thank goodness somebody somewhere thought about it and got it
right.  Good looking out, Andy.


   (1)111  * 2^0                                              1111
+ (1)000  * 2^-2                         =              +  0010
------------------------                                    -----------
                                                                    10001,  represented as  (1)000 chop 1
   

Heh - the full scale thing was a simplification for an easy example with just two samples; I do know how it works in detail (indeed, I wrote a floating-point library back in the days before the processors did it internally).

Paul

So two identical files subtracted from each other don't equal zero?

Right...

A file subtracted from itself equals zero.  Two files subtracted from their sum will often leave a residue.

Two files subtracted from their sum will often leave a residue.

Is that all he's worried about? Time he got a life...

No, I don’t think there is any more important questions. This is what I originally expected, before David (in the other thread) pointed out that mixing two files was simple addition and should not generate values that overflowed 32 bit float. I think the crux is that generating files in 32 bit float more or less fills up all the available bits with something, thus there is overflow when two such files are mixed.

I don’t think SteveG would argue that quantization errors are impossible in 32 bit float, only that they are just too small to matter in any practical sense. Why he gets different results with a different program version, when David does not, is different mystery.

Therefore, by first saving my created dither file as 24 bit, then using that in the 24 to 16 conversion and subsequent operations, I can remove all traces/results of the dither, save the fact that it uncorrelated the 24 bit to 16 bit conversion quantization errors.

This might not be perfect if what was being converted to 16 bits was the result of a lot of mixing and mastering, but in that case any music file data below 24 bits (when working in 32 bit floating format) is probably not going to audibly effect the outcome. In the immediate case, this is supposed to be an original 24 bit recording, with no post recording processing, therefore nothing below 24 bits, even when working in CE’s 32 bit format.

Somebody correct me if I'm wrong, but I don't recall any version of CEP having Spectral View.

My CEP version 1.0 and 1.2a had spectral view... Don't think they made a special one for me, I'm not that important 

Somebody correct me if I'm wrong, but I don't recall any version of CEP having Spectral View.

My CEP version 1.0 and 1.2a had spectral view... Don't think they made a special one for me, I'm not that important 

And that's why I asked someone to correct me.  Thanks for that.  It's been many years since I've opened up any CEP program. 

No, I don’t think there is any more important questions.

Except it is not a 'question'.  Without infinite precision, things are not infinitely precise!  At some point in human intellectual development probably a novel concept but can now, for most people, be retired from 'news of weird'

after reading younglove's post (thanks by the way) I had the 'ah ha!' epiphany and realized that, not surprisingly (deciphering this stuff is, for me, a bit like waiting for Godot) I had entirely missed the point.

while string theory might permit parallel universes with different rules even in everyday life neither subtraction nor division are commutative (for that matter, somewhat applicable to 'programing' arithmetic operations, concantation is not additively commutative).  And in real world dividing a dinner tab among seven individuals (also imprecise by definition) is seldom novel enough to warrant inquiry, let alone fisticuffs

and AndyH, that without infinite precision one does not achieve infinite precision is neither, at this moment in history, a particularly novel observation nor a 'general audio' issue, though it is perhaps unfortunate that, for most people, that is an obvious observation.  In 'general audio' inaudible . . . not merely 'generally' inaudible, not merely inaudible to cats (with generally speaking better hearing then dogs), but, probably (or at least speculatively) thermodynamically inaudible. . . , perhaps also obviously, becomes 'good enough'  and I still stand by the assertion that the 'audio' tool CE2K was not the appropriate tool for this particular inquiry

It would be nice to have Audition 3 for its better tools, as well as a system capable of making use of it, but that just isn’t possible. I know there are also other tools, hardware and software, that could be very useful. While life can be frustrating, I see no reason to ignore everything that interests me just because I can’t afford the best.

However much it might seem to some, I am not confused about the instant issue. I expected the differences. This thread arose because someone else, with a different version of CoolEdit, did not find them and, logically enough under certain other considerations, thought they should not be there -- rather as SteveG did. This thread was not about the main issue of that other inquiry, just a hope to gain some insight about a sticking point on the way to the real goal. That has been accomplished.

Obviously, it is often perfectly feasible to have complete precision within limited circumstances. The proper kind of files can be mixed and manipulate, then subtracted completely, digital silence being the reasonably expected, and the observed, result.

That ultimate goal had to do with looking at the intrinsic differences between certain aspects of a 16 bit conversion of a 24 bit recording and the original 24 bit recording itself. Dither swamps those differences, so can it be taken out of the picture? It can -- to a large extent. Here, the observation that precision is incomplete is very relevant, but that fact was not unknown or ignored.

Does the resolution of difference, to the extent that it is possible, have any useful meaning? Can we a priori make that decision without knowing what that difference is? I remember reading long ago, in a history on science, a tale about some medieval monks who loved to debate “intellectual” subjects to pass long winter evenings (probably because they were quite without women to distract them). One fiercely debated topic was the number of teeth possessed by a mule, which the monks attempted to resolve by various logical constructs. When a novice pointed out that they had some mules on hand, and thus could easily count their teeth, he was soundly beaten.

I remember reading long ago, in a history on science, a tale about some medieval monks who loved to debate “intellectual” subjects to pass long winter evenings (probably because they were quite without women to distract them). One fiercely debated topic was the number of teeth possessed by a mule, which the monks attempted to resolve by various logical constructs. When a novice pointed out that they had some mules on hand, and thus could easily count their teeth, he was soundly beaten.

Obviously the monks' "logical constructs" weren't logical enough to find the simple solution to their debate.  They were more interested in the debate rather than the answer.  Stupid monks. 

It would be nice to have Audition 3 for its better tools, as well as a system capable of making use of it, but that just isn’t possible. I know there are also other tools, hardware and software, that could be very useful. While life can be frustrating, I see no reason to ignore everything that interests me just because I can’t afford the best.

except nothing I said implied need for new computer or expensive programs for accurate bit by bit comparison of two binaries:

a = 100
b = 200
bit = 1
Loop, 32 {
   if ((a & bit) != (b & bit)) {
      MsgBox, bits %A_Index% are different
   }
   bit <<= 1
}

is outline that can be used (maybe.  Any code I actually write has potential to introduce 'out of range' ice 9 elements)

part of the point is that -168 dB s/n is, for humans, whales, cats, no longer 'audio' so it's not surprising that audio optimized apps might be less then concerned

main point was that if you needed to compare two files bit by bit no variation of CE or AA would, necessarily, be my first choice.  And while I'm sure there are frightfully expensive forensic (for example) packages out there I'm pretty sure there are cheap to free hex editors that should work nicely.

If one thought there was a problem with the maths of CE2k (even if it only showed up in data out of audio range) one would not, typically, use CE2K to do the analysis.

With Younglove's explanation it seems probable that the initial post rose from a deliberately articulated event with more in common with numerology of  con men making change then anything that makes sense to me concerning audio analysis

but once again if it's the math of the program then something like: http://exeicon.com/hex-comparison/ with (with free trial) would produce a highly precise comparison of the files (no new computer, no new expensive software, just ability to actually investigate issue raised)

Obviously, it is often perfectly feasible to have complete precision within limited circumstances. The proper kind of files can be mixed and manipulate, then subtracted completely, digital silence being the reasonably expected, and the observed, result.

The 'limited' is limit of precision. . .  so? complete precision except for the those circumstances that limit it!  and applying operations that are not commutative (or necessarily associative) and expressing interest that results demonstrate that those operations are not commutative, falls beneath the limit of an interesting observation, let alone rising to 'no more important' question status

but outside of initial specific issue is simply word juggling to shift the goal posts . . . 'precision' is going to be limited by your 'circumstances' and is therefore not 'complete' but 'limited'  reason for changing from 8 to 12 to 16 to 20 to floating point bitdepth was to improve precision of operations  I am unaware of anyone positing infinite precision for even 32 bit floating point . . . it has been suggested that the inevitable 'rounding' errors will tend to land outside the range of audio detection

Does the resolution of difference, to the extent that it is possible, have any useful meaning? Can we a priori make that decision without knowing what that difference is? I remember reading long ago, in a history on science, a tale about some medieval monks who loved to debate “intellectual” subjects to pass long winter evenings (probably because they were quite without women to distract them). One fiercely debated topic was the number of teeth possessed by a mule, which the monks attempted to resolve by various logical constructs. When a novice pointed out that they had some mules on hand, and thus could easily count their teeth, he was soundly beaten.

it is obviously long past time for me to exit this thread and while I suspect responding to this quote borders on the churlish . . . what the hell

even here I suspect that AndyH might miss, more or less thoroughly, how the scholastic approach to analysis differs from the alchemists (and knowing what I do of human nature I am fairly certain that interchanges among the practitioners probably got colorful)

what I find amusing here is not that AndyH seems to identify with the scholastics but that it has taken him so long (seven years and counting) to introduce the intimation of violence for those that fail to recognize infinite brilliance

(yes, I'm well aware that irony and sarcasm do not travel well . .. but again what the hell . . . somewhere buried in this thread is the thread of functional stand up comedy routine: is the sky 'blue' or does it merely appear to be 'blue'? And would Samuel L. Jackson resent the offer to play John L. Hooker as the mephistopheles for the second half of 20th century? Or: if Marilyn Monroe and Mike Tyson had produced an il lle·git·i·mate love child, would that baby have been able to grow to defeat Mohammed Alli . . . all weighty considerations)