The dynamic range of 16 bits

[Christer]

Well, I have nothing extra to say about this at the moment, but
since Kuei failed to follow the moderators order to start a new
thread on this topic if wishing to continue the discussion, I
decided to do so for him.

The discussion so far on this topic will soon appear in a thread
near you, if the moderators manage to lift it out of the thread
it appeared in.

Moderators: Please feel free to remove this post after moving
the discussion to this thread, since it is merely a place-holder.

[ALW]

Kuei was wrong.

If you turn off dither in Cooledit and generate a 0dBfs 1k sine wave, then attenuate by 96 dB you get, as one would predict, a 1k residual, with high distortion content.

Add dither and distortion drops dramatically, as one would predict.

I'll post pics later on.

Andy.

[SY]

You don't even need software. Look at the numbers: the lowest nonzero encodable number in a 16 bit system is 1. Or if you want to be pedantic, 0000000000000001. The highest encodable number is 65,536, or for the pedantic, 1111111111111111. So toggle the 1 on and off. That's the lowest signal encodable without dither or other signal processing. Toggle the 65,536 on and off. That's the biggest encodable signal, same qualification.

The dynamic range is defined as the ratio between biggest and smallest encodable signal. Converting to dB, 20 x log (65536) = 96.3 dB.

Whether or not you can figure out how to toggle these bits in a particular piece of software is irrelevant. Anyone can put the numbers in a file and use a graphing program.

[Steve Eddy]

Originally posted by SY
You don't even need software.

Kuei's approach here rather reminds me of John Bedini's patent for his "Bedini Clarifier," a device which simply spins a CD around above an electromagnet.

In Bedini's patent, he claims that doing this not only rearranges the data on the CD, but also performs data compression on it. In other words, not only is the data on the CD different, it's relocated as well.

To prove that this was the case, he took a Kodak PhotoCD and copied an image off the CD onto his computer's hard drive. He then ran the CD on his Clarifier and then copied the same file to another directory on his computer's hard drive.

Then he pulled each file into a graphics program and converted them to PostScript files. He then he pulls the PostScript files into a text editor and shows that one file contains more lines of text than the other with the smaller one being from the Clarified CD. He then uses the text editor to compare the differences between the two and showed a number of differences between the two files.

Thus, by way of this experiment, he proved that his Clarifier was indeed rearranging and performing data compression just as he claimed.

So I thought I'd try a similar experiment.

I took a CD of some photographs and I copied one of the files onto my hard drive. I took the CD out of the drive, held it in my hand and looking sternly at it said:

"I claim that I am the Great and Powerful Steve Eddy. I know all. I see all. I command all. The Great and Powerful Steve Eddy commands the data on this disc to compress and rearrange itself. So shall it be written. So shall it be done."

I put the CD back in the drive and copied the same file over to another directory on my hard drive.

Then I pulled each file into CorelXARA! and converted them into PostScript files.

I didn't bother using a text editor. I just had to look at the file sizes. And indeed, the file sizes were different. Then I ran the DOS file compare utility (fc) on them and found that there were considerable differences between the two files.

I'd just proved beyond any doubt that I truly am the Great and Powerful Steve Eddy. That I know all. That I see all. That I command all.

And if I get any more lip from Kuei, I'm going to turn him into a Bose Wave Radio and donate it to the local senion citizens home so they can all listen to Paul Harvey.

Oh, and if anyone can't afford a Bedini Clarifier, just let me know and I'll be happy to use my powers to perform data rearrangement and compression on their CDs remotely.

se

[ThorstenL]

Koinichiwa,

Originally posted by ALW
Kuei was wrong.

If you turn off dither in Cooledit and generate a 0dBfs 1k sine wave, then attenuate by 96 dB you get, as one would predict, a 1k residual, with high distortion content.
Andy.

Okay, lets do this again. Dither is of. Cooledit is set to 16 Bit. I post step by step pictures.

Go to:

http://www.cooledit.com/

Download and install Cooledit 2.1.

Turn of Dither:

http://groups.yahoo.com/group/Thunderstone_audiophile/files/96db/0 Turn off Dither.jpg


Make a sinewave:

Select 44.1KHz & 16 Bit in the intermeidate Dialogue:

http://groups.yahoo.com/group/Thunde...ect 16 Bit.jpg

Use 1KHz, 0dbfs as settings for sinewave:

http://groups.yahoo.com/group/Thunderstone_audiophile/files/96db/1 Generate Wave.jpg

Zoom in so we something of the waveform, just to confirm we did what we wanted to:

http://groups.yahoo.com/group/Thunde...s Waveform.jpg

Attenuate the waveform by 91db:

http://groups.yahoo.com/group/Thunde...nuate 91db.jpg

Zoom in on the level axis only into the botton of the dynamic range - no signal at any funloving level, I only zoomed down to -102dbfs as this suffices:

http://groups.yahoo.com/group/Thunde... - silence.jpg

I must admit this to be probably the most involved procedure for generating digital silence, but digital silence it generates, like it or not.

Please demonstrate where I went wrong (apart from leaving dither off, which was the whole point of the excercise - I KNOW what dither does and how it works). Everything done can be followed readily, easily and reliably by ANYONE who cares to experiment.

If you cannot tell me what "I did wrong", then explain why a 96db dynamic range system cannt encode anything below -90.3dbfs without dither.

I am waiting.



Sayonara

[Fred Dieckmann]

Starting with the disclaimer that I hate audio charlatans with a well documented passion and will include the claims of Mr. Bedini on data compression, I will admit to hearing the effect of demagnetizing, with a bulk tape eraser, some (not all) CDs. I believe it might have something to do with the permeability of the inks on the label. I will put on my boots for the oncoming load of "knowledge" from an expert on electromagnetics as well. In his defense (knowledge, not character), I will point out Mr. Bedini knows how to design amplifiers but lacked the expertise in marketing them possessed by some gifted individuals.

[jwb]

Originally posted by SY
You don't even need software. Look at the numbers: the lowest nonzero encodable number in a 16 bit system is 1. Or if you want to be pedantic, 0000000000000001. The highest encodable number is 65,536, or for the pedantic, 1111111111111111.

The pedantic would disagree. The full scale level in 16-bit PCM is 32767, or 15 bits with a sign. So full scale positive is 0x7FFF and full scale negative is 0x8000. The dynamic range is therefore 20*log(32767) or 90.3dB

The maximum thoeretical dynamic range of a PCM system is 20 times the base-10 logarithm of 2 raised to the power of one less than the number of bits, or 20*log(2^(bits - 1)).

Originally posted by Kuei Yang Wang

If you cannot tell me what "I did wrong", then explain why a 96db dynamic range system cannt encode anything below -90.3dbfs without dither.

It is not 96dB. It is 90.3dB

[Steve Eddy]

Originally posted by Kuei Yang Wang
If you cannot tell me what "I did wrong", then explain why a 96db dynamic range system cannt encode anything below -90.3dbfs without dither.

I am waiting.

What you did wrong was assume you were getting nothing but digital silence by simply eyeballing the screen.

Here's the frequency spectrum of 1 second of digital silence:

<center>
<img src="http://www.q-audio.com/images/silence.jpg">
</center>

Here's the frequency spectrum of 1 second of a 1kHz sinewave at 0dBFS:

<center>
<img src="http://www.q-audio.com/images/fullscale.jpg">
</center>

Here's the frequency spectrum of that same full scale sinewave with the amplitude set for -90.3dB:

<center>
<img src="http://www.q-audio.com/images/90point3db.jpg">
</center>

And here is the frequency spectrum of that same full scale sinewave with the amplitude set for -96dB:

<center>
<img src="http://www.q-audio.com/images/96db.jpg">
</center>

Well it looks like HTML tags are dinked up again so you'll just have to copy and paste the URLs above to see them.

se

[SY]

That's not correct, I believe. Using a sign bit (say, zero for negative and 1 for positive in the first bit position) is no different than using any other bit, with one minor exception. That exception is the degeneracy of 1000000000... and 00000000.... So the system still has 65,534 other nondegenerate codes. You can still toggle the LSB on and off:

0000000000000000,
0000000000000000,
0000000000000001,
0000000000000001,
0000000000000000,
0000000000000000,
0000000000000001,
0000000000000001,
,
.
.
.
and compare that signal to
0111111111111111,
0111111111111111,
1111111111111111,
1111111111111111,
0111111111111111,
0111111111111111,
1111111111111111,
1111111111111111.
.
.
.

Sure, the signing introduces an offset in the signal (ie, the low level signal is not symmetrical about the zero voltage axis), but, so what? The ratio of the biggest to the smallest signal encodable is still 96 dB, unless you restrict things to only those signals that are symmetric about DC. And that's an unneccessary constraint.

[SY]

Steve, do you know the old Penn and Teller "God of Carbonation" trick?