On Dec 9, 2009, at 9:02 PM, Brian Willoughby wrote:
The problem with this whole thread is that there is no downgrade in
fidelity with the conversion method used by CoreAudio. All the rest
of the comments assume that there is a superior method when there
really isn't one.
Bjorn proposes in his blog that there are two good choices for
conversion methods. I'll call them A and B. Method A is used by
Apple in CoreAudio. Method B is the 'asymmetrical' option. Bjorn
claims that they are both good, with each method having specific
benefits and drawbacks. The problem is that Bjorn's hypothesis has
not been peer-reviewed, and does not stand up to basic mathematical
principles. Bjorn's own tests do not reveal the flaws in method B
because his tests are incomplete and do not have a solid basis.
It's true I didn't have my BLOG ENTRY pear reviewed, LoL.
As for not having a solid basis, I admit I did not concern myself with
the mathematical details which are complex, and not really worth my
time for a blog entry. They have been covered in academia, I believe
and I'll see if I can find a reference. I did, however, address the
apparent asymmetry of 'Method B', as you call it, in passing.
In a nutshell, Bjorn's asymmetrical conversion introduces non-linear
distortion by processing positive values differently than negative
values.
Depends on what you mean by linear. I am talking about dynamic systems
and that's what I tested. Would you consider a 1-bit converter non-
linear? It is only linear because of dither, after all, and in the
same way Method B is linear.
Ross' comments about CPU efficiency are a diversion from the fact
that all processing on the distorted waveforms would make this
distortion irreversible.
Agreed.
Bjorn's tests only happen to reverse this non-linear distortion for
the one special case where no processing is done on the audio, which
is clearly not an option for someone using Logic, or even for
someone combining music and system sounds on the same interface.
This is a best-case, actually. There is no sense in measuring
distortion after DSP.
Thus, asymmetrical conversion would not work for most application,
and since you can't use different conversions for different
applications you much use the CoreAudio conversion (or equivalent).
That's the trouble with designing your own tests, because your
assumptions are masked by the implementation of your tests.
Now I am being flamed for running tests! I have to admit I didn't see
that one coming! :)
[snip]
For anyone interested in the other flaws in Bjorn's blog entries:
* Bjorn claims that when A/D converters clip around -.5 dBFS, that
it's equivalent to (2^n)-.5, which is completely false. This
clipping happens entirely in the analog domain, before quantization
to digital codes, so it is not equivalent to (2^n)-.5 because the
converter is still based on 2^n. What happens before the A/D
conversion cannot be precisely equated to binary math. These
comments show a lack of understanding of the A/D process as well as
mathematics.
Wow, that wasn't my claim at all. My claim, perhaps poorly written,
was that full-scale positive less 1 is less than .5 dBFS on most
converters and that experience has shown that many converters happen
to clip around .5 dBFS. Meaning that there may not be much point in
optimizing the heck out of +1 anyway, which is actually a point in the
2^N (your) camp's favor. I admit this could have been better written.
* Bjorn claims that +1 occurs in the real world, but that's not
true. The only real world is the analog world, and no A/D converter
allows the +1 value. In the virtual world of VST synths, +1 is
certainly possible, but only a problem for developers who try to get
closer to the 24-bit maximum than the 16-bit maximum. In contrast,
hardware DSP chips have embedded sine wave ROM tables which e.g.
only span +/- 32766. No attempt is made to reach +32767, and
certainly not -32768, because 2 LSBs of headroom is immaterial.
32766 is only 0.00053 dB below full scale, and nobody really cares
to risk clipping for such a miniscule gain in signal level. A 24-
bit variant would just synthesize waveforms without getting so close
to clipping. 24-bit codes could be a tiny fraction louder than 16-
bit codes, but not enough to warrant the risk of clipping with 16-
bit audio interfaces. In other words, Bjorn is actually looking at a
real issue worthy of discussion, but the suggested solution is
entirely wrong.
Actually, that was an answer to a question. The question was "The
question is whether or not this matters.... My Opinion?". So you admit
I was looking at a real issue worthy of discussion (presumably,
whether or not +1 matters), and I think it's pretty clear I was
stating an opinion (that it does matter) rather than stating fact. So
we disagree. I don't think stating my opinion makes the entry
factually "flawed" if it is labeled as such.
* Bjorn synthesizes sine waves and then tests distortion outputs,
all without specifying the source for the sine data. The standard C
math library sin() and cos() functions use linear interpolation to
produce the values, and so Bjorn's original data has distortion from
the start. In other words, those are not pure sine waves! Thus,
the tests that are cited are nothing more than fun and pretty
pictures, and they are certainly not mathematical proofs of the bad
assumptions made about asymmetrical conversions.
Look at the diagrams. I show the original sine waves in the FFT plots
subject to the exact same analysis. You have to look closely because
they are just spikes. No noise. This is a standard analysis
methodology used, for example, when analyzing dither.
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