Jon Harris wrote:


They *WON'T* have the same SNR. THAT'S THE POINT!

Right! Halfscale with have 6dB less SNR than full-scale.

Not necessarily. Its perfectly possible that the same bit pattern will result
from both input sequences or an even cleaner one from the half scale if the
full scale contains more noise. I guess your assuming that quantization error
is the only source of noise in the original signal. Even if that were true the
difference in error from half-scale to full scale is insignificant compared to
the amount of error added when going down to one bit - so few bits will end up
different that you won't be able to hear the difference. If I understand
Randy's dither algo the amount of dither added decreases proportional to the
final bit depth. Again that means when you get down to one bit so few bits
will be changed you won't be able to hear the difference.
By the way, I'm surprised that no one picked up on the fact that coal doesn't
crackle when it burns :-}

-jim


-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 100,000 Newsgroups - 19 Different Servers! =-----

"jim" wrote in message
...


Jon Harris wrote:


They *WON'T* have the same SNR. THAT'S THE POINT!

Right! Halfscale with have 6dB less SNR than full-scale.

Not necessarily. Its perfectly possible that the same bit pattern will result
from both input sequences or an even cleaner one from the half scale if the
full scale contains more noise.

I thought we were talking about the difference between full-scale and half-scale
sine waves?

I guess your assuming that quantization error
is the only source of noise in the original signal. Even if that were true the
difference in error from half-scale to full scale is insignificant compared to
the amount of error added when going down to one bit - so few bits will end up
different that you won't be able to hear the difference. If I understand
Randy's dither algo the amount of dither added decreases proportional to the
final bit depth.

I think you have that backwards. The fewer bits, the more dither you need, so
dither is inversely proportional to final bit depth.

Again that means when you get down to one bit so few bits
will be changed you won't be able to hear the difference.

I think you are a bit confused about the way dithered quantization works. Given
a clean input signal, properly dithered quantization to N bits adds noise based
on N alone--it is NOT depended on the signal. Now if you quantize a signal
identical to the first one in every way except 6dB quieter again to N bits
(assuming the original signal has bits than N) you will have the same amount
of quantization noise, but since the original signal was 6dB softer, you have
6dB worse SNR. It really works, I've tried it!

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback, say
60dB. You can still hear the recorded signal, but there is plenty of tape hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor just
like tape hiss. (The only difference is that the frequency response of the tape
noise may be different than the dither noise. In fact, the digital designer can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital sound
like analog!

"jim" wrote in message
...


Jon Harris wrote:


They *WON'T* have the same SNR. THAT'S THE POINT!

Right! Halfscale with have 6dB less SNR than full-scale.

Not necessarily. Its perfectly possible that the same bit pattern will result
from both input sequences or an even cleaner one from the half scale if the
full scale contains more noise.

I thought we were talking about the difference between full-scale and half-scale
sine waves?

I guess your assuming that quantization error
is the only source of noise in the original signal. Even if that were true the
difference in error from half-scale to full scale is insignificant compared to
the amount of error added when going down to one bit - so few bits will end up
different that you won't be able to hear the difference. If I understand
Randy's dither algo the amount of dither added decreases proportional to the
final bit depth.

I think you have that backwards. The fewer bits, the more dither you need, so
dither is inversely proportional to final bit depth.

Again that means when you get down to one bit so few bits
will be changed you won't be able to hear the difference.

I think you are a bit confused about the way dithered quantization works. Given
a clean input signal, properly dithered quantization to N bits adds noise based
on N alone--it is NOT depended on the signal. Now if you quantize a signal
identical to the first one in every way except 6dB quieter again to N bits
(assuming the original signal has bits than N) you will have the same amount
of quantization noise, but since the original signal was 6dB softer, you have
6dB worse SNR. It really works, I've tried it!

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback, say
60dB. You can still hear the recorded signal, but there is plenty of tape hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor just
like tape hiss. (The only difference is that the frequency response of the tape
noise may be different than the dither noise. In fact, the digital designer can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital sound
like analog!

"jim" wrote in message
...


Jon Harris wrote:


They *WON'T* have the same SNR. THAT'S THE POINT!

Right! Halfscale with have 6dB less SNR than full-scale.

Not necessarily. Its perfectly possible that the same bit pattern will result
from both input sequences or an even cleaner one from the half scale if the
full scale contains more noise.

I thought we were talking about the difference between full-scale and half-scale
sine waves?

I guess your assuming that quantization error
is the only source of noise in the original signal. Even if that were true the
difference in error from half-scale to full scale is insignificant compared to
the amount of error added when going down to one bit - so few bits will end up
different that you won't be able to hear the difference. If I understand
Randy's dither algo the amount of dither added decreases proportional to the
final bit depth.

I think you have that backwards. The fewer bits, the more dither you need, so
dither is inversely proportional to final bit depth.

Again that means when you get down to one bit so few bits
will be changed you won't be able to hear the difference.

I think you are a bit confused about the way dithered quantization works. Given
a clean input signal, properly dithered quantization to N bits adds noise based
on N alone--it is NOT depended on the signal. Now if you quantize a signal
identical to the first one in every way except 6dB quieter again to N bits
(assuming the original signal has bits than N) you will have the same amount
of quantization noise, but since the original signal was 6dB softer, you have
6dB worse SNR. It really works, I've tried it!

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback, say
60dB. You can still hear the recorded signal, but there is plenty of tape hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor just
like tape hiss. (The only difference is that the frequency response of the tape
noise may be different than the dither noise. In fact, the digital designer can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital sound
like analog!

"jim" wrote in message
...


Jon Harris wrote:


They *WON'T* have the same SNR. THAT'S THE POINT!

Right! Halfscale with have 6dB less SNR than full-scale.

Not necessarily. Its perfectly possible that the same bit pattern will result
from both input sequences or an even cleaner one from the half scale if the
full scale contains more noise.

I thought we were talking about the difference between full-scale and half-scale
sine waves?

I guess your assuming that quantization error
is the only source of noise in the original signal. Even if that were true the
difference in error from half-scale to full scale is insignificant compared to
the amount of error added when going down to one bit - so few bits will end up
different that you won't be able to hear the difference. If I understand
Randy's dither algo the amount of dither added decreases proportional to the
final bit depth.

I think you have that backwards. The fewer bits, the more dither you need, so
dither is inversely proportional to final bit depth.

Again that means when you get down to one bit so few bits
will be changed you won't be able to hear the difference.

I think you are a bit confused about the way dithered quantization works. Given
a clean input signal, properly dithered quantization to N bits adds noise based
on N alone--it is NOT depended on the signal. Now if you quantize a signal
identical to the first one in every way except 6dB quieter again to N bits
(assuming the original signal has bits than N) you will have the same amount
of quantization noise, but since the original signal was 6dB softer, you have
6dB worse SNR. It really works, I've tried it!

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback, say
60dB. You can still hear the recorded signal, but there is plenty of tape hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor just
like tape hiss. (The only difference is that the frequency response of the tape
noise may be different than the dither noise. In fact, the digital designer can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital sound
like analog!

Tachyon writes:

On 2004-05-21, Jon Harris wrote:
"jim" wrote in message
...


Randy Yates wrote:

The noise will be high, but my intuition tells me you will be able to hear
the signal (at least one that is at a high level) in the noise. Almost
certainly one would be able to hear a full-scale sinewave in such noise.

Why would the scale of the sine wave make any difference or maybe I
misunderstand what you're saying.

It is simply a signal-to-noise ratio issue. Much noise is added by the
dithering/quantizing process. If the original signal is quite loud, it will
still be recognizable above the noise floor. If it is very low level, it will
be further buried by the noise. I did a quick experiment, and a full scale
sinewave quanitzed with dither was easily heard. I decreased the level and
somewhere around 20-30dB down, you really start to lose it. I was actually
suprised by how low you could go and still make out the tone in the noise.

Here is an experiment I did.

There are 16 repetitions of the well-known 909 kick drum, mixing triangular noise
in varying amounts and quantizing to 1 bit. Each hit of the drum doubles the
noise. It's really interesting to look at with a wave editor, as well as to
listen. At the low-noise version, you hear a "mean" kick sound. At the noisy end,
you hear more dynamic range and more noise. I personally like it best with
about 3/4 of an LSB added. BTW, the subjective volume seems quieter when
more noise is added:

http://www.gweep.net/~shifty/audio/1...ction/re02.wav

best listened to in loop mode!!

Cool! But... You made the dang thing so short! I mean, bszzzt and it's done!
--
% Randy Yates % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC % sliding, it's magic."
%%% 919-577-9882 %
%%%% % 'Living' Thing', *A New World Record*, ELO
http://home.earthlink.net/~yatescr

Tachyon writes:

On 2004-05-21, Jon Harris wrote:
"jim" wrote in message
...


Randy Yates wrote:

The noise will be high, but my intuition tells me you will be able to hear
the signal (at least one that is at a high level) in the noise. Almost
certainly one would be able to hear a full-scale sinewave in such noise.

Why would the scale of the sine wave make any difference or maybe I
misunderstand what you're saying.

It is simply a signal-to-noise ratio issue. Much noise is added by the
dithering/quantizing process. If the original signal is quite loud, it will
still be recognizable above the noise floor. If it is very low level, it will
be further buried by the noise. I did a quick experiment, and a full scale
sinewave quanitzed with dither was easily heard. I decreased the level and
somewhere around 20-30dB down, you really start to lose it. I was actually
suprised by how low you could go and still make out the tone in the noise.

Here is an experiment I did.

There are 16 repetitions of the well-known 909 kick drum, mixing triangular noise
in varying amounts and quantizing to 1 bit. Each hit of the drum doubles the
noise. It's really interesting to look at with a wave editor, as well as to
listen. At the low-noise version, you hear a "mean" kick sound. At the noisy end,
you hear more dynamic range and more noise. I personally like it best with
about 3/4 of an LSB added. BTW, the subjective volume seems quieter when
more noise is added:

http://www.gweep.net/~shifty/audio/1...ction/re02.wav

best listened to in loop mode!!

Cool! But... You made the dang thing so short! I mean, bszzzt and it's done!
--
% Randy Yates % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC % sliding, it's magic."
%%% 919-577-9882 %
%%%% % 'Living' Thing', *A New World Record*, ELO
http://home.earthlink.net/~yatescr

Tachyon writes:

On 2004-05-21, Jon Harris wrote:
"jim" wrote in message
...


Randy Yates wrote:

The noise will be high, but my intuition tells me you will be able to hear
the signal (at least one that is at a high level) in the noise. Almost
certainly one would be able to hear a full-scale sinewave in such noise.

Why would the scale of the sine wave make any difference or maybe I
misunderstand what you're saying.

It is simply a signal-to-noise ratio issue. Much noise is added by the
dithering/quantizing process. If the original signal is quite loud, it will
still be recognizable above the noise floor. If it is very low level, it will
be further buried by the noise. I did a quick experiment, and a full scale
sinewave quanitzed with dither was easily heard. I decreased the level and
somewhere around 20-30dB down, you really start to lose it. I was actually
suprised by how low you could go and still make out the tone in the noise.

Here is an experiment I did.

There are 16 repetitions of the well-known 909 kick drum, mixing triangular noise
in varying amounts and quantizing to 1 bit. Each hit of the drum doubles the
noise. It's really interesting to look at with a wave editor, as well as to
listen. At the low-noise version, you hear a "mean" kick sound. At the noisy end,
you hear more dynamic range and more noise. I personally like it best with
about 3/4 of an LSB added. BTW, the subjective volume seems quieter when
more noise is added:

http://www.gweep.net/~shifty/audio/1...ction/re02.wav

best listened to in loop mode!!

Cool! But... You made the dang thing so short! I mean, bszzzt and it's done!
--
% Randy Yates % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC % sliding, it's magic."
%%% 919-577-9882 %
%%%% % 'Living' Thing', *A New World Record*, ELO
http://home.earthlink.net/~yatescr

Tachyon writes:

On 2004-05-21, Jon Harris wrote:
"jim" wrote in message
...


Randy Yates wrote:

The noise will be high, but my intuition tells me you will be able to hear
the signal (at least one that is at a high level) in the noise. Almost
certainly one would be able to hear a full-scale sinewave in such noise.

Why would the scale of the sine wave make any difference or maybe I
misunderstand what you're saying.

It is simply a signal-to-noise ratio issue. Much noise is added by the
dithering/quantizing process. If the original signal is quite loud, it will
still be recognizable above the noise floor. If it is very low level, it will
be further buried by the noise. I did a quick experiment, and a full scale
sinewave quanitzed with dither was easily heard. I decreased the level and
somewhere around 20-30dB down, you really start to lose it. I was actually
suprised by how low you could go and still make out the tone in the noise.

Here is an experiment I did.

There are 16 repetitions of the well-known 909 kick drum, mixing triangular noise
in varying amounts and quantizing to 1 bit. Each hit of the drum doubles the
noise. It's really interesting to look at with a wave editor, as well as to
listen. At the low-noise version, you hear a "mean" kick sound. At the noisy end,
you hear more dynamic range and more noise. I personally like it best with
about 3/4 of an LSB added. BTW, the subjective volume seems quieter when
more noise is added:

http://www.gweep.net/~shifty/audio/1...ction/re02.wav

best listened to in loop mode!!

Cool! But... You made the dang thing so short! I mean, bszzzt and it's done!
--
% Randy Yates % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC % sliding, it's magic."
%%% 919-577-9882 %
%%%% % 'Living' Thing', *A New World Record*, ELO
http://home.earthlink.net/~yatescr

Randy Yates wrote:
"Geoff Wood" -nospam writes:

I was alluding to the resultant signal being an asymetrical
bitstream, like a PWM signal.

I have no idea what you mean.


That's for sure. It was a jest. You may end up with something like:

001001000000110111111100011111111110000

.....which looks to me like a PWM signal, that clearly has no relationship
whatsoever to the original signal.

Yes I know that a serial bitstrem is not what goes into a DA or out of a PCM
word . It was a jest, but equally validly pointing out the silliness of the
"1-bit' sound quality suggestion.

geoff



Though I did qualify that it bears no relationship to any
encoded signal.

What is "it"?

One "1", followed by one "0", then two "1"s followed by a "0" looks
PWM to me.

How so? It doesn't match any definition of PWM that I know of. When I
talk about PWM, I mean, e.g., the type of signal shown in figure one
of

http://www.embedded.com/story/OEG20010821S0096

Randy Yates wrote:
"Geoff Wood" -nospam writes:

I was alluding to the resultant signal being an asymetrical
bitstream, like a PWM signal.

I have no idea what you mean.


That's for sure. It was a jest. You may end up with something like:

001001000000110111111100011111111110000

.....which looks to me like a PWM signal, that clearly has no relationship
whatsoever to the original signal.

Yes I know that a serial bitstrem is not what goes into a DA or out of a PCM
word . It was a jest, but equally validly pointing out the silliness of the
"1-bit' sound quality suggestion.

geoff



Though I did qualify that it bears no relationship to any
encoded signal.

What is "it"?

One "1", followed by one "0", then two "1"s followed by a "0" looks
PWM to me.

How so? It doesn't match any definition of PWM that I know of. When I
talk about PWM, I mean, e.g., the type of signal shown in figure one
of

http://www.embedded.com/story/OEG20010821S0096

Randy Yates wrote:
"Geoff Wood" -nospam writes:

I was alluding to the resultant signal being an asymetrical
bitstream, like a PWM signal.

I have no idea what you mean.


That's for sure. It was a jest. You may end up with something like:

001001000000110111111100011111111110000

.....which looks to me like a PWM signal, that clearly has no relationship
whatsoever to the original signal.

Yes I know that a serial bitstrem is not what goes into a DA or out of a PCM
word . It was a jest, but equally validly pointing out the silliness of the
"1-bit' sound quality suggestion.

geoff



Though I did qualify that it bears no relationship to any
encoded signal.

What is "it"?

One "1", followed by one "0", then two "1"s followed by a "0" looks
PWM to me.

How so? It doesn't match any definition of PWM that I know of. When I
talk about PWM, I mean, e.g., the type of signal shown in figure one
of

http://www.embedded.com/story/OEG20010821S0096

Randy Yates wrote:
"Geoff Wood" -nospam writes:

I was alluding to the resultant signal being an asymetrical
bitstream, like a PWM signal.

I have no idea what you mean.


That's for sure. It was a jest. You may end up with something like:

001001000000110111111100011111111110000

.....which looks to me like a PWM signal, that clearly has no relationship
whatsoever to the original signal.

Yes I know that a serial bitstrem is not what goes into a DA or out of a PCM
word . It was a jest, but equally validly pointing out the silliness of the
"1-bit' sound quality suggestion.

geoff



Though I did qualify that it bears no relationship to any
encoded signal.

What is "it"?

One "1", followed by one "0", then two "1"s followed by a "0" looks
PWM to me.

How so? It doesn't match any definition of PWM that I know of. When I
talk about PWM, I mean, e.g., the type of signal shown in figure one
of

http://www.embedded.com/story/OEG20010821S0096

Jon Harris wrote:

"jim" wrote in message
...


Jon Harris wrote:


They *WON'T* have the same SNR. THAT'S THE POINT!

Right! Halfscale with have 6dB less SNR than full-scale.

Not necessarily. Its perfectly possible that the same bit pattern will result
from both input sequences or an even cleaner one from the half scale if the
full scale contains more noise.


I thought we were talking about the difference between full-scale and half-scale
sine waves?


I guess your assuming that quantization error
is the only source of noise in the original signal. Even if that were true the
difference in error from half-scale to full scale is insignificant compared to
the amount of error added when going down to one bit - so few bits will end up
different that you won't be able to hear the difference. If I understand
Randy's dither algo the amount of dither added decreases proportional to the
final bit depth.


I think you have that backwards. The fewer bits, the more dither you need, so
dither is inversely proportional to final bit depth.


Again that means when you get down to one bit so few bits
will be changed you won't be able to hear the difference.


I think you are a bit confused about the way dithered quantization works. Given
a clean input signal, properly dithered quantization to N bits adds noise based
on N alone--it is NOT depended on the signal. Now if you quantize a signal
identical to the first one in every way except 6dB quieter again to N bits
(assuming the original signal has bits than N) you will have the same amount
of quantization noise, but since the original signal was 6dB softer, you have
6dB worse SNR. It really works, I've tried it!

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback, say
60dB. You can still hear the recorded signal, but there is plenty of tape hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor just
like tape hiss. (The only difference is that the frequency response of the tape
noise may be different than the dither noise. In fact, the digital designer can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital sound
like analog!

Relative to full scale on 15 bits plus sign, one bit is 90 dB down.
bringing that back to full scale is the equivalent of sign extending
down to all the bits. It needs some mental contortions to decide what to
make of it.

Dither is properly done using an amplitude equal to the least-
significant bit. When only one bit is significant, does that mean adding
100% noise? If not, what?

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Jon Harris wrote:

"jim" wrote in message
...


Jon Harris wrote:


They *WON'T* have the same SNR. THAT'S THE POINT!

Right! Halfscale with have 6dB less SNR than full-scale.

Not necessarily. Its perfectly possible that the same bit pattern will result
from both input sequences or an even cleaner one from the half scale if the
full scale contains more noise.


I thought we were talking about the difference between full-scale and half-scale
sine waves?


I guess your assuming that quantization error
is the only source of noise in the original signal. Even if that were true the
difference in error from half-scale to full scale is insignificant compared to
the amount of error added when going down to one bit - so few bits will end up
different that you won't be able to hear the difference. If I understand
Randy's dither algo the amount of dither added decreases proportional to the
final bit depth.


I think you have that backwards. The fewer bits, the more dither you need, so
dither is inversely proportional to final bit depth.


Again that means when you get down to one bit so few bits
will be changed you won't be able to hear the difference.


I think you are a bit confused about the way dithered quantization works. Given
a clean input signal, properly dithered quantization to N bits adds noise based
on N alone--it is NOT depended on the signal. Now if you quantize a signal
identical to the first one in every way except 6dB quieter again to N bits
(assuming the original signal has bits than N) you will have the same amount
of quantization noise, but since the original signal was 6dB softer, you have
6dB worse SNR. It really works, I've tried it!

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback, say
60dB. You can still hear the recorded signal, but there is plenty of tape hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor just
like tape hiss. (The only difference is that the frequency response of the tape
noise may be different than the dither noise. In fact, the digital designer can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital sound
like analog!

Relative to full scale on 15 bits plus sign, one bit is 90 dB down.
bringing that back to full scale is the equivalent of sign extending
down to all the bits. It needs some mental contortions to decide what to
make of it.

Dither is properly done using an amplitude equal to the least-
significant bit. When only one bit is significant, does that mean adding
100% noise? If not, what?

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Jon Harris wrote:

"jim" wrote in message
...


Jon Harris wrote:


They *WON'T* have the same SNR. THAT'S THE POINT!

Right! Halfscale with have 6dB less SNR than full-scale.

Not necessarily. Its perfectly possible that the same bit pattern will result
from both input sequences or an even cleaner one from the half scale if the
full scale contains more noise.


I thought we were talking about the difference between full-scale and half-scale
sine waves?


I guess your assuming that quantization error
is the only source of noise in the original signal. Even if that were true the
difference in error from half-scale to full scale is insignificant compared to
the amount of error added when going down to one bit - so few bits will end up
different that you won't be able to hear the difference. If I understand
Randy's dither algo the amount of dither added decreases proportional to the
final bit depth.


I think you have that backwards. The fewer bits, the more dither you need, so
dither is inversely proportional to final bit depth.


Again that means when you get down to one bit so few bits
will be changed you won't be able to hear the difference.


I think you are a bit confused about the way dithered quantization works. Given
a clean input signal, properly dithered quantization to N bits adds noise based
on N alone--it is NOT depended on the signal. Now if you quantize a signal
identical to the first one in every way except 6dB quieter again to N bits
(assuming the original signal has bits than N) you will have the same amount
of quantization noise, but since the original signal was 6dB softer, you have
6dB worse SNR. It really works, I've tried it!

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback, say
60dB. You can still hear the recorded signal, but there is plenty of tape hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor just
like tape hiss. (The only difference is that the frequency response of the tape
noise may be different than the dither noise. In fact, the digital designer can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital sound
like analog!

Relative to full scale on 15 bits plus sign, one bit is 90 dB down.
bringing that back to full scale is the equivalent of sign extending
down to all the bits. It needs some mental contortions to decide what to
make of it.

Dither is properly done using an amplitude equal to the least-
significant bit. When only one bit is significant, does that mean adding
100% noise? If not, what?

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Jon Harris wrote:

"jim" wrote in message
...


Jon Harris wrote:


They *WON'T* have the same SNR. THAT'S THE POINT!

Right! Halfscale with have 6dB less SNR than full-scale.

Not necessarily. Its perfectly possible that the same bit pattern will result
from both input sequences or an even cleaner one from the half scale if the
full scale contains more noise.


I thought we were talking about the difference between full-scale and half-scale
sine waves?


I guess your assuming that quantization error
is the only source of noise in the original signal. Even if that were true the
difference in error from half-scale to full scale is insignificant compared to
the amount of error added when going down to one bit - so few bits will end up
different that you won't be able to hear the difference. If I understand
Randy's dither algo the amount of dither added decreases proportional to the
final bit depth.


I think you have that backwards. The fewer bits, the more dither you need, so
dither is inversely proportional to final bit depth.


Again that means when you get down to one bit so few bits
will be changed you won't be able to hear the difference.


I think you are a bit confused about the way dithered quantization works. Given
a clean input signal, properly dithered quantization to N bits adds noise based
on N alone--it is NOT depended on the signal. Now if you quantize a signal
identical to the first one in every way except 6dB quieter again to N bits
(assuming the original signal has bits than N) you will have the same amount
of quantization noise, but since the original signal was 6dB softer, you have
6dB worse SNR. It really works, I've tried it!

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback, say
60dB. You can still hear the recorded signal, but there is plenty of tape hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor just
like tape hiss. (The only difference is that the frequency response of the tape
noise may be different than the dither noise. In fact, the digital designer can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital sound
like analog!

Relative to full scale on 15 bits plus sign, one bit is 90 dB down.
bringing that back to full scale is the equivalent of sign extending
down to all the bits. It needs some mental contortions to decide what to
make of it.

Dither is properly done using an amplitude equal to the least-
significant bit. When only one bit is significant, does that mean adding
100% noise? If not, what?

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

"Jerry Avins" wrote in message
...
Jon Harris wrote:

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback,
say
60dB. You can still hear the recorded signal, but there is plenty of tape
hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same
level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor
just
like tape hiss. (The only difference is that the frequency response of the
tape
noise may be different than the dither noise. In fact, the digital designer
can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital
sound
like analog!

Relative to full scale on 15 bits plus sign, one bit is 90 dB down.
bringing that back to full scale is the equivalent of sign extending
down to all the bits. It needs some mental contortions to decide what to
make of it.

Dither is properly done using an amplitude equal to the least-
significant bit. When only one bit is significant, does that mean adding
100% noise? If not, what?

For audio, ideal dither is noise with a triangular probability distribution with
peak-to-peak magnitude equal to 2 LSB's of the new word size. This means, as
you suspected, that a whole lot of noise is added when quantizing to 1 bit! The
theory has been extensively worked out in various AES journal articles and PhD
thesis such as this one: http://audiolab.uwaterloo.ca/~rob/phd.html

"Jerry Avins" wrote in message
...
Jon Harris wrote:

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback,
say
60dB. You can still hear the recorded signal, but there is plenty of tape
hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same
level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor
just
like tape hiss. (The only difference is that the frequency response of the
tape
noise may be different than the dither noise. In fact, the digital designer
can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital
sound
like analog!

Relative to full scale on 15 bits plus sign, one bit is 90 dB down.
bringing that back to full scale is the equivalent of sign extending
down to all the bits. It needs some mental contortions to decide what to
make of it.

Dither is properly done using an amplitude equal to the least-
significant bit. When only one bit is significant, does that mean adding
100% noise? If not, what?

For audio, ideal dither is noise with a triangular probability distribution with
peak-to-peak magnitude equal to 2 LSB's of the new word size. This means, as
you suspected, that a whole lot of noise is added when quantizing to 1 bit! The
theory has been extensively worked out in various AES journal articles and PhD
thesis such as this one: http://audiolab.uwaterloo.ca/~rob/phd.html

"Jerry Avins" wrote in message
...
Jon Harris wrote:

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback,
say
60dB. You can still hear the recorded signal, but there is plenty of tape
hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same
level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor
just
like tape hiss. (The only difference is that the frequency response of the
tape
noise may be different than the dither noise. In fact, the digital designer
can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital
sound
like analog!

Relative to full scale on 15 bits plus sign, one bit is 90 dB down.
bringing that back to full scale is the equivalent of sign extending
down to all the bits. It needs some mental contortions to decide what to
make of it.

Dither is properly done using an amplitude equal to the least-
significant bit. When only one bit is significant, does that mean adding
100% noise? If not, what?

For audio, ideal dither is noise with a triangular probability distribution with
peak-to-peak magnitude equal to 2 LSB's of the new word size. This means, as
you suspected, that a whole lot of noise is added when quantizing to 1 bit! The
theory has been extensively worked out in various AES journal articles and PhD
thesis such as this one: http://audiolab.uwaterloo.ca/~rob/phd.html

"Jerry Avins" wrote in message
...
Jon Harris wrote:

I'll use my analog cassette tape analogy one more time. Imagine recording a
very low level signal to a cassette tape. Then boost the gain on playback,
say
60dB. You can still hear the recorded signal, but there is plenty of tape
hiss.
Now imagine doing the same thing again, except with the original signal 6dB
softer. Boost by the same 60dB and the tape hiss is still at the same
level,
but the original signal is 6dB softer, hence 6dB worse SNR. Dithered
quantization works THE SAME WAY! The dither (noise) creates a noise floor
just
like tape hiss. (The only difference is that the frequency response of the
tape
noise may be different than the dither noise. In fact, the digital designer
can
choose the sound of the noise floor using noise shaping.)

BTW, that's one of the big breakthroughs about dither--it makes digital
sound
like analog!

Relative to full scale on 15 bits plus sign, one bit is 90 dB down.
bringing that back to full scale is the equivalent of sign extending
down to all the bits. It needs some mental contortions to decide what to
make of it.

Dither is properly done using an amplitude equal to the least-
significant bit. When only one bit is significant, does that mean adding
100% noise? If not, what?

For audio, ideal dither is noise with a triangular probability distribution with
peak-to-peak magnitude equal to 2 LSB's of the new word size. This means, as
you suspected, that a whole lot of noise is added when quantizing to 1 bit! The
theory has been extensively worked out in various AES journal articles and PhD
thesis such as this one: http://audiolab.uwaterloo.ca/~rob/phd.html

Geoff Wood wrote:

One "1", followed by one "0", then two "1"s followed by a "0" looks PWM to
me.

Only in a NRZ system... :-)

-- Rick

Geoff Wood wrote:

One "1", followed by one "0", then two "1"s followed by a "0" looks PWM to
me.

Only in a NRZ system... :-)

-- Rick

Geoff Wood wrote:

One "1", followed by one "0", then two "1"s followed by a "0" looks PWM to
me.

Only in a NRZ system... :-)

-- Rick