16=20 or the mathematics of RCA

[Christer]

I was just reading on the case of an RCA CD I bought recently,
finding the text

"Digitally remastered using UV22 Super CD Encoding, which
delivers 20-bit resolution and quality on any standard CD
player"

Let's see now, it is a standard CD which means only 16 bits
can be encoded and the sampling frequency is also standardized
so there is no possibility of storing more information that way.
So where do the extra four bits come from??? Are they broadcast
from RCA directly to my CD player???

[Netlist]

Hi Christer
Google is a wonderful thing.
It reveals a lot about your question.
http://www.google.be/search?hl=nl&ie...Encoding&meta=

/Hugo

[Christer]

Thanks Hugo,

My question was actually, at least to some extent, rhetorical,
since I assumed it was mostly marketing hype. It seems,
however, from the links you found that there is more
to it than I thought. I did not quite understand the details and
how it actually differed from other similar methods, though.
Is it just added noise restricted to a narrow band around half
the sampling frequency?

Strictly information-theoretically it is, of course, still a false
claim that it gives 20-bit resolution.

Anyway, the CD sounds good. Whether it sounds like 16 bits
or 20 bits or 17 and half I cannot say.

[Netlist]

As I'm not a 'digital' man, (hardly analog) I also have no clue what exactly happens.

The nice part seems to be that one doesn’t need a different cd player to benefit from the technology unlike SACD.

/Hugo

[Christer]

Hugo,

Well, I do have a clue, and I think I understand the basic
principle behind all these similar techniques, although I
don't understand the details.

A very simplified explanation, as I understand it, is as follows.
(It was meant to be brief, but after typing it I realized it wasn't
very brief, so bear with me.)

The brain is very good at recognizing patterns. Especially it is
good at recogninzing sound buried below the noise floor.
(I have read somewhere that trained radio surveillance
personell can often hear and understand speech as far down
as 40dB below the noise floor!! Of course the noise floor is
pretty high then.) Now, take a sine wave digitalized to 16 bits
and randomly add +1 or -1 to each sample. Although not quite
a pure sine wave anymore, we have no problem recognizing it
as one. These small errors in the samples will (if heard at all)
be perceived as some kind of noise.

Now consider a 20-bit digitalization of the sine wave, which we
are to convert to 16 bits. If we just truncate the four lowest bits
or round off to the nearest 16-bit number, a certain 20-bit value
will always be mapped to the same 16-bit value, so we lose
4 bits of information. Now, add som noise to the 20-bit source
before converting it, and suppose we convert by rounding off
to the nearest 16-bit number. Because of the added noise,
a particular sample value (before the noise) will sometimes
be rounded off downwards, sometimes upwards. However,
if the value is close to the nearest lower 16-bit value it will be
rounded off downwards more often than upwards, and if it is
closer to the nearest upper 16-bit value it will be rounded off
upwards more often. Each sample in the converted version
still contains only 16 bits of information, so what's the deal?

Well, lets take this 16-bit encoding see what we can do with it.
To simplify matters, let's assume the frequency of the sine wave
is a multiple of the sampling frequency, so samples occur at the
same positions in each cycle. The sine wave is periodic so let's
take 16 succesive cycles and compare "the same" sample in
each of these cycles. Although it should have the same value
in all of the cycles, it doesn't since we added noise before
converting to 16 bits. This is exactly what we want, however.
Since we are looking at 16 cycles simultaneously, we can take
the average of the values this sample has in the 16 cycles. Since
we took 16 cycles and 2^4=16, we have essentially recovered
4 extra bits of precision by looking at many cycles, instead of
one. Of course, we do not truly recover the exact original value
since the noise we added was random, so we get more than
16 bits, but not quite 20 bits of precision.

This assumed a periodic sine wave which repeats itself exactly
from cycle to cycle. Music isn't quite like that, but still, sounds
are periodic even if they do not repeat exactly. The simple
algorithm of taking the average of 16 cycles does not work
anymore, but it gives some idea of how information can be
recovered. Fortunately, our brain is very good at finding
patterns of this kind.

[Netlist]

Euuhhh, ???

Nice explanation.
I will re-read this tomorrow, promised!!
......and try to understand it......

/Hugo

[Pjotr]

Hi Christer,

Yes our brain is unsurpassed when it comes to pattern recognition. But do make adding noise, and in that sense “blurring” the original information, it more intelligible?

You can test it for yourself: In most word processors an drawing programs you can switch “smoothing” on and off. On large characters it makes sense, but on very small characters smoothing on makes these characters less intelligible. You can leave the smoothing better to your brain in the latter case.

Cheers

[Christer]

Pjotr,

Of course it does not always work to add noise, and when it
works it has to be the right "type" of noise.

Don't get me started on computer fonts!!! MS Truetype fonts
is a hate object of mine. It is totally misguided. A font which
looks nice on paper is usually totally unsuitable to be read
on a computer screen, since the latter has so much lower
resolution than printers. Very simple, typewriter-style fonts,
on the other hand are often easy to read on a screen, although
they look ugly on paper. (For some strange reason they never
looked ugly on paper until people started to use computers
and laser printers. ). This is also one of several reasons
why I dislike WYSIWYG word processors like Word and similar
and think of these as misguided too, but that's a different story
I'd better not get into now.

[Pjotr]

Hi Christer,

Don’t misunderstand me, I do not want to go in a discussion about fonts. But there is some resemblance with your original question. It is all about sampling rate and signal slope. The whole thing of adding noise relies on “averaging”. This works well on low frequencies, or better said signals with less steep slopes, because there are enough samples to average. But on higher frequencies and steeper slopes? Sony’s “Super bitmapping” relies on the same basics. To me the added resolution sounds artificial, but not necessarily bad

[Christer]

Originally posted by Pjotr
Hi Christer,

Don’t misunderstand me, I do not want to go in a discussion about fonts. But there is some resemblance with your original question.

Don't worry, I did take it the way you intended, I just couldn't
resist the opportunity to rant a bit about the font issue. I am
of the opinion that MS often makes a lot of ill-judged decisions
that prevents us from making use of the fact that we actually
have a very powerful too in front of us. Easy to use for novices
and occasional users perhaps, but often a painful obstacle
to work efficiently.

It is all about sampling rate and signal slope. The whole thing of adding noise relies on “averaging”. This works well on low frequencies, or better said signals with less steep slopes, because there are enough samples to average. But on higher frequencies and steeper slopes? Sony’s “Super bitmapping” relies on the same basics. To me the added resolution sounds artificial, but not necessarily bad

I didn't necessarily mean that these methods work well in
practice, I have not had the opportunity to do any listening
comparisons, and I don't understand the theory well enough
either. I hope my attempt at a "popular" explanation of the
basic idea wasn't to way off, though. Please feel free to point
out if I made any serious errors in the explanation.

BTW, did you understand how this UV22 technique works? Is
as I think, that a narrow band of noise is added around fs/2?