The dynamic range of 16 bits

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Re: Gratuitous image time.......

Jocko Homo said:
I'm gonna burn for this one, but it is supposed to be a joke. And not to be taken seriously or personally.

I'll say you'll burn in hell. That picture's WAY outdated!

Here's something a little more recent.
 

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diyAudio Retiree
Joined 2002
just the voltage out for the for the possible range of digital input values

"PS. the tables are, of course not pure data, but for the purpose
of dynamic range they are."

It Depends on What Your Definition of the Word Bits, Is...........


"I did not have sax with that woman."
 

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The dynamic range is:

110 dB.....A-weighted. Does that answer your question? Point is:

It is capable of 2^20, as that is the LSB step.

For 10 points............

Carl Palmer......who went on with the keyboard player to.......Atomic Rooster.....and then joined:

Emerson, Lake, and Palmer.

3 "Moes" to ya'. Nyuk, nyuk.

For your 10 points:

What band (from your area, hint, hint......) had every song on one of their albums released as a single?


Jocko
 
Jocko, I'm impressed. And if Eric is right about my hearing, I can blame it on a particular ELP concert during their Brain Salad Surgery tour.

And for your question, I have no idea. Showing my age?

Arthur Brown, sheesh. You know they actually make Arthur Brown references on "Iron Chef"? He must still be some kind of cult figure in Japan. Whatever happened to him?
 
what would be the zero signal....

EC8010 said:
But what if I apply a sine wave with a peak to peak amplitude of 1 LSB with a DC offset of 1/2 LSB to a 16 bit signed bit system? I get my predicted S/N ratio.

Are you sure of your presicted S/N ratio in this configuration? How about tell us how to express 'Zero' signal in this system?
 
Re: Steve the Naive

SY said:
Are you familiar with the story of Alfred Russel Wallace and John Hampden?

Of course I'm familiar with the story of Alfred Russel Wallace and John Hampden! Who do you think you're talking to here? I am The Great and Powerful Steve Eddy. I know all. I see all. I command all. (he says while surreptitiously closing down the Google session)

Wanna bet? :)

se
 
Re: I wonder how many bits can dance on the head of a pin?

Fred Dieckmann said:
[BGee I always thought you had to run the digital audio through a DAC to hear or measure the analog signal. If some one has found a way to listen to the data direct I would be very interested !!!!
[/B]

While I agreed on the need for a DAC in my previous reply, I
realized later that maybe it isn't. It depends on your definition
of DAC. Philips actually worked on "digital speakers" maybe
20 years, or so, ago. As I understood the idea they had a
flat membrane, probably between two perforated
permanent magnets. The membrane had metal traces on it,
similar to inductors etched on a PCB. There was one trace for
each bit, 16 in total, and their R and L properties were choosen
to give their appropriate bit weights when fed with the same
voltage. Of course, this is in a sense a DAC, but it is an
integrated speaker and DAC, not doing the conversion entirely
in the electric domain.

Well, you said you would be interested, so I thought I'd better
tell you.
 
Koinichiwa,

SY said:
The offset in my example is not 0.5 volt, it's 0.5 times the voltage corresponding to the LSB. That's a lot different. Unless you're using the CD player hooked to Ol' Sparky.

EC8010 said:
But what if I apply a sine wave with a peak to peak amplitude of 1 LSB with a DC offset of 1/2 LSB to a 16 bit signed bit system? I get my predicted S/N ratio.

Steve Eddy said:
So, can we finally put this one to bed?

The sheer tedium of this thread shure beats even having to clean a large latrine with a toothbrush.... (yes, I know that of which I talk).

Okay, the DC offset chestnut. I calulated first a percentage of DC offset to a percentage, as cooledit likes the DC offset in percent.

To get a relative value for the value of the LSB I calculated:
1/65536 = 0.0000152587890625

For 1/2 LSB divided that by 2:

0.0000152587890625/2 = 0.00000762939453125

For the percentage of 1/2 LSB I multilplied that with 100:

0.00000762939453125 * 100 = 0.000762939453125%

For use in Cooledit I choose to round to 0.00076%.

I then proceedded to generate a 16 Bit, 44100Hz sample rate tone (dither off):

An externally hosted image should be here but it was not working when we last tested it.
http://groups.yahoo.com/group/Thunderstone_audiophile/files/96dboff/1.jpg

I next selected a 10s sinewave tone, 1KHz, 0dbfs and entered my 0.00076% DC offset (yes, I did enter the 6 even if you don't see it on the screen):

An externally hosted image should be here but it was not working when we last tested it.
http://groups.yahoo.com/group/Thunderstone_audiophile/files/96dboff/2.jpg

Just to make sure we have a nice sinewave I zoomed in and we note a slight clipping of the sinewave top:

An externally hosted image should be here but it was not working when we last tested it.
http://groups.yahoo.com/group/Thunderstone_audiophile/files/96dboff/3.jpg

I then applied the same -91db attenuation as previously done in the other example:

An externally hosted image should be here but it was not working when we last tested it.
http://groups.yahoo.com/group/Thunderstone_audiophile/files/96dboff/4.jpg

Now looking again, voila, again a straight line, despite 1/2 LSB DC offset applied earlier:

An externally hosted image should be here but it was not working when we last tested it.
http://groups.yahoo.com/group/Thunderstone_audiophile/files/96dboff/5.jpg

But from the sidelines the peasants where shouting "but there is something on the FFT", so I made sure I also looked at the FFT:

An externally hosted image should be here but it was not working when we last tested it.
http://groups.yahoo.com/group/Thunderstone_audiophile/files/96dboff/6.jpg

Again, flatline, digital silence.

I can get the same sort of display Eddy San demonstrated by truning dither on, but that is in effect noiseshaping which increases the resolution towards lower frequencies and reduces it at higher ones, plus it raises the noisefloor and the raised noisefloor again scuppers the "96db Dynamic range" as you reduce it with dither to somewhere between 90db (where it was before) and 93db.

Someone else said to me about this thread "deprogramming a member of a cult is easier" and I'm forced to agree. Other than sophistry, badly applied math and outright forgery nothing has been presented to show anything different to my contention.

I repeat, ANYONE can download Cooledit and repeat my experiments and I have documented all settings and steps in thishere thread.

THIS IS EVIDENCE that materially supports my contention and does not support the irrational belief into the Emporers new 96db Cloth's.

As I have commented in other threads, personal beliefs can be held to any funloving point. Facts are something different.

We have two options. The makers and programmers of any major waveedit program I have, plus a significant number of other programers (and of course myself) are wrong.

Or a clique of a few people who have read enough to fall into the "a little knowledge is a dangerous thing" category, have major stakes in their credibility and rarely IF EVER present empirical (aka practical results) are wrong.

I suggest to the august reader to make their own experiments and to draw their own conclusions as to the reality of what is being proposed here by the various sides.

Sayonara
 
Koinichiwa,

Kuei Yang Wang said:
Koinichiwa,

I then applied the same -91db attenuation as previously done in the other example:

An externally hosted image should be here but it was not working when we last tested it.
http://groups.yahoo.com/group/Thunderstone_audiophile/files/96dboff/4.jpg

Looking at this made me aware of a checkbox named "DC Bias Adjust". I made sure there was no adjustment of DC bias to 0, still no output.

Reintroducing the 0.00076% Bias with a -91db attenuation produces an extremely distorted waveform where there is much more energy concentrated in the distortion products then in the main (1KHz) tone illustrating (again) that "tone" is actually below THD&N and thus below the dynamic range.

Attenuating with 1/2 LSB Bias by -96db results (again) in digital silence.

No matter how we cut it. We need to raise the noisefloor to -90db to show any output below -90db, except that it's not any valid output. And still, no dither, no -96db.

Again, if you don't believe, instead of arguing that the legless dog really has four legs and is an excellent hunting dog too, JUST DOWNLOAD THE SOFTWARE AND MAKE THE EXPERIMENT.

COME ON - TAKE THE -96db TEST. WHAT DO YOU HAVE TO LOOSE.

Sayonara
 
Koinichiwa,

SY said:
Look at the data file, if this program generates one. Is the LSB toggling on and off? If not, RTFM.

When attenuating by -91db with 1/2 LSB offset - yes. The FFT shows with an inordinate wide window (65536 Samples or > 1sec length) -99db for the resulting 1KHz and -100db for the 2nd harmonic.

Looking at the waveform you get short positive going impulses with their top reaching the -90db and their bottom at digital silence.

So, you have managed to encode a -91dbfs tone with an amplitude error of 8db for the fundamental and a larger RMS sum of noise and distortion than the fundamental.

An externally hosted image should be here but it was not working when we last tested it.
http://groups.yahoo.com/group/Thunderstone_audiophile/files/96dboff/7.jpg

Here the FFT. Remember, what you are seeing is suppsed to be -91dbfs with 1/2LSB DC offset:

An externally hosted image should be here but it was not working when we last tested it.
http://groups.yahoo.com/group/Thunderstone_audiophile/files/96dboff/8.jpg

NOW, CAN WE FINALLY put this urban myth of the 96db dynamic range of CD to bed?

The facts are:

1) Theoretical peak dynamic range is 90.3db, theoretical RMS dynamic range is 87.3db

2) Practical Peak dynamic range with dither is around 90db, so no change (it just does not sound as bad).

3) Practical RMS dynamic range (to be comparable with analogue system measurements) is 87db or if we account for quantisation noise even lower (up to 6db).

4) As practical all analogue system have a significant headroom we ned to account for the added headroom requirements of CD and knock 14db off (recommended headroom according to Bob Katz) or in my experience at least 10db (difference between RMS and peaks on music in the loiudes passages).

This means when comparing analogue Tape or LP in a realistic "like for like" usable dynamic range view CD has up between 67db and 77db dynamic range, putting it in the worst case view on bare parity with a quiet LP and in the best case still below the best of analogue tape. This BTW was my original contention, out of which this -96db or -90db discussion arose.

BTW, non of the above has any particular impact on the simple mathematical formula 2^16=65536=96db. Except of course that the 96db figure which seems to have become an orthodox tenet of "objectivist" Audio faith (even if it is objectively "wrong" when applied to audio) is inapplicable without adjustment or qalification to Audio systems.

Before (ANY OF) you argue any more and spew any more utter loblocks (as they say on planent anagramia), go and do the darn experiment, fer goodness sake!!!

Sayonara
 
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