Nyquist theorem states that a non-variant signal freqency can be reproduced
that is 1/2 the sample rate. Unfortunately, music that is invariant is not
terribly interesting. Thus, the common wisdom that 44.1KHz sampling can
reproduce 22 KHz music is not true.

A seminal paper from MIT shows that distortion related to sampling must
consider both the sample rate and the target word size. For today's
CDs--that is 16 bits. Thus, according to this paper, a minimum of 8X
frequency is required--10X is better. Working backwards, that means that CD
technology can only reproduce, at best, 5.5 KHz before distortion starts to
enter in. This is independant of the construction of filters and assumes a
boxcar filter (impossible in real life.)

Other solutions have worked hard to reduce this problem by oversampling,
adding bits, etc. All these solutions smooth the distortion created by the
original system, but they can not add information back in that is lost.
What they can do is create better sounding music by smoothing out the
jaggies in the distortion.

"tubesforall" = a deranged liar


Nyquist theorem states that a non-variant signal freqency can be
reproduced that is 1/2 the sample rate.


** WRONG !!!!

It says that ANY signal with frequency components not exceeding a certain
bandwidth can be *exactly* reproduced by sampling it at a rate of double
that bandwidth.


Unfortunately, music that is invariant is not terribly interesting. Thus,
the common wisdom that 44.1KHz sampling can reproduce 22 KHz music is not
true.


** A stupid false conclusion based on the stupid false stating of Nyquist
above.



A seminal paper from MIT shows that distortion related to sampling must
consider both the sample rate and the target word size.


** Correct - the Nyquist sampling theorem assumes accurate samples.


For today's CDs--that is 16 bits.


** Which is **highly accurate** sampling.


Thus, according to this paper, a minimum of 8X frequency is required--10X
is better.


** Pure horse manure.


Working backwards, that means that CD technology can only reproduce, at
best, 5.5 KHz before distortion starts to enter in.


** More asinine bull****.

CD players can reproduce 19 kHz and 20 kHz simultaneously with no IM at
all.

Proof of perfect high frequency linearity.



Other solutions have worked hard to reduce this problem by oversampling,
adding bits, etc.


** You are a miserable, bloody liar.

**** off !!!!



.............. Phil

Nyquist assumes that all you want is to reproduce is a sine wave. Music is
not all sine waves.


Stu

"audiodir"

Nyquist assumes that all you want is to reproduce is a sine wave. Music is
not all sine waves.


** BULL**** !!!!!!!!

The theorem is true for any possible wave form, or combinations of
waveforms and varying in any possible way.


Stupid





............. Phil

"Phil Allison" wrote

The theorem is true for any possible wave form, or combinations of
waveforms and varying in any possible way.

Only whilst remaining waveforms. I don't think music quite
qualifies. Waves are about sameness, music is about change.

cheers, Ian

Ian Iveson wrote:
"Phil Allison" wrote

The theorem is true for any possible wave form, or combinations of
waveforms and varying in any possible way.

Only whilst remaining waveforms. I don't think music quite
qualifies. Waves are about sameness, music is about change.

There is another problem - the spectrum width... Even 1 Hz square wave has
an extremely wide spectrum, infinite for an ideal square wave. So the sound
might be right but all the attacks are distorted in some way.

And don't forget, Kotelnikov's theorem is not about the signal frequency,
its about signal _spectrum_ . So it is possible to record a 20 KHz
squarewave with 44/16, but when played back it'll become a perfect sinus...

---
************************************************** ****************
* KSI@home KOI8 Net The impossible we do immediately. *
* Las Vegas NV, USA Miracles require 24-hour notice. *
************************************************** ****************

"Ian Iveson" = another nut case pommy prick


"Phil Allison"
The theorem is true for any possible wave form, or combinations of
waveforms and varying in any possible way.

Only whilst remaining waveforms. I don't think music quite qualifies.
Waves are about sameness, music is about change.



** The Nyquist sampling theorem applies to ANY signal - not merely nice
steady waveforms as seen on a scope screen.

A signal is a *constantly changing* voltage that only has **one** value
at any instant in time. This **one** value can be regularly sampled as
accurately and as often as you like in order to create a precise record of
how the the signal varied over time.

The sampling theorem establishes that for an *exact* replication of ANY
signal the number of samples need not be infinite, as one might suppose,
but needs only to just exceed a number equal to twice the number of cycles
of the highest frequency component of the particular signal during the time
it is being sampled.

The phrase "any possible waveform" includes the unpredictable waveforms of
random noise and natural sounds.

Capice now - ****head ???





............. Phil

On Wed, 09 Mar 2005 18:06:59 GMT, "Ian Iveson"
wrote:

"Phil Allison" wrote

The theorem is true for any possible wave form, or combinations of
waveforms and varying in any possible way.

Only whilst remaining waveforms. I don't think music quite
qualifies. Waves are about sameness, music is about change.

So is progress................

The bottom line is of course that CD produces *vastly* fewer audible
artifacts than does vinyl. That's why the first mass acceptance of CD
was in the *classical* arena, where listeners tend to be more
critical, and also know what the instruments *should* sound like.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

Ian Iveson wrote:

"Phil Allison" wrote

The theorem is true for any possible wave form, or combinations of
waveforms and varying in any possible way.

Only whilst remaining waveforms. I don't think music quite
qualifies. Waves are about sameness, music is about change.

Waves are never the same when you are sailing.....

Sme for electronics. waves are signals going up and down in level
relative to some
usually fixed voltage.

But one could look at a pink noise source and yea, waves are seen, but
each
wave is different from the one that preceeded it, and to the one after
it.
Musical waves ain't much different to noise waves, the only difference
is that there
are more clumps of what seem to be repetitive waves with a smaller
spectrum
or F content than for noise.

One can purchase a CD with pink noise recorded on it.
There won't be too much content above 21 kHz though.

Patrick Turner.





cheers, Ian

"Ian Iveson" wrote in message
k...
"Phil Allison" wrote

The theorem is true for any possible wave form, or combinations of
waveforms and varying in any possible way.

Only whilst remaining waveforms. I don't think music quite
qualifies. Waves are about sameness, music is about change.

cheers, Ian


Not so. Any repeating waveform can be represented by set of sinusoids
(fundamental plus harmonics, i.e. Fourier analysis.) Thus, given a
proper bandwidth limiting antialiasing filter, any waveform can be
sampled and reproduced exactly by sampling at twice the highest
harmonic frequency.
Cheers,
Roger

"audiodir" wrote in news:mGRWd.73204$Dc.23025
@trnddc06:

Nyquist assumes that all you want is to reproduce is a sine wave. Music is
not all sine waves.


Stu



That depends on what you consider music. One could have a recording of
square waves as an effect but there are no naturally occuring square waves.
I believe there are some bass tracks on some pop CD;s that are square waves
but that only occurs electronically and in the studio.

Most square waves on CD's are low frequencies so they get reproduced quite
well. Conversly, the LP is quite incapable of producing square waves. The
ristime is so fast that the corners would be quickly stripped off.

I recall when this topic came up once before, someone threatened to write a
sonata for function generator and drum. I don't think it ever happened
though.

r

"R" wrote in message
...
| "audiodir" wrote in news:mGRWd.73204$Dc.23025
| @trnddc06:
|
| Nyquist assumes that all you want is to reproduce is a sine wave. Music
is
| not all sine waves.
|
|
| Stu
|
|
|
| That depends on what you consider music. One could have a recording of
| square waves as an effect but there are no naturally occuring square
waves.
| I believe there are some bass tracks on some pop CD;s that are square
waves
| but that only occurs electronically and in the studio.
|
| Most square waves on CD's are low frequencies so they get reproduced quite
| well. Conversly, the LP is quite incapable of producing square waves.
The
| ristime is so fast that the corners would be quickly stripped off.
|
| I recall when this topic came up once before, someone threatened to write
a
| sonata for function generator and drum. I don't think it ever happened
| though.
|
| r

luckily-those square wave aren't good cutted in vinyl ;
when you have veeeery pricey TT with almost cutter lathe quality ,
reproducing error will be of same magnitude as in cutting process,but with
exactly opposite meaning.........
ha-everything is in clever coding-encoding technology !

awesome TT is always better than awesome CD
lucky for me -I have awesome TT ,and I'm free off all this ****ty blah blah
CD against LP

btw-I also have awesome CD


--
--
.................................................. ........................
Choky
Prodanovic Aleksandar
YU

"don't use force, "don't use force,
use a larger hammer" use a larger tube
- Choky and IST"
- ZM
.................................................. ...........................

On Mon, 07 Mar 2005 05:30:58 GMT, "audiodir"
wrote:

Nyquist assumes that all you want is to reproduce is a sine wave. Music is
not all sine waves.

Fourier demonstrates that *any* waveform, including music, can be
represented as a series of superimposed sinewaves. Hence, Nyquist and
Shannon are correct in their postulations. While music may not
*appear* to be sinewaves, it can be so treated for the purposes of
reproduction. Bottom line of course is that digital audio works, and
reproduces music more accurately than any other system.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

Behold, Stewart Pinkerton scribed on tube chassis:

On Mon, 07 Mar 2005 05:30:58 GMT, "audiodir"
wrote:

Nyquist assumes that all you want is to reproduce is a sine wave. Music
is not all sine waves.

Fourier demonstrates that *any* waveform, including music, can be
represented as a series of superimposed sinewaves. Hence, Nyquist and
Shannon are correct in their postulations. While music may not *appear*
to be sinewaves, it can be so treated for the purposes of reproduction.
Bottom line of course is that digital audio works, and reproduces music
more accurately than any other system.

And after going through any compression, other than lossless (FLAC or
APE), makes the whoke kit-and-kaboodle math moot.

--
Gregg "t3h g33k"
http://geek.scorpiorising.ca
*Ratings are for transistors, tubes have guidelines*

Fourier demonstrates that *any* waveform, including music, can be
represented as a series of superimposed sinewaves. Hence, Nyquist and
Shannon are correct in their postulations. While music may not *appear*
to be sinewaves, it can be so treated for the purposes of reproduction.
Bottom line of course is that digital audio works, and reproduces music
more accurately than any other system.


And after going through any compression, other than lossless (FLAC or
APE), makes the whoke kit-and-kaboodle math moot.

CDs don't use compression (mp3 sort or the sort of thing
done by radio stations). The sample frequency and bit depth
was chosen such that the errors fall outside normal human
hearing ability.

I have no doubt as to the Fourier statements and theory, but that is also
based on unlimited data. It would seem that in the case where there is an
upper limit, then the data available becomes truncated as you approach that
limit, making recreation of a waveform much more difficult.
Perhaps the problem is not so much with the Nyquist theory as its
application. After all, a DAC has to set the parameters of what waveform it
seeks to recreate. I believe the Spectral DAC had an option to set different
algorithms to use in the decoding process. The waveforms generated are not
dissimilar to the differences seen in a cadcam system when asked to
interpolate a curve over various points.
While most music is a series of sine waves, there are a lot of impulses and
other unusual waveforms (think of the 'grundge' associated with rock
electric guitars and the inherent distortion those instruments can produce).
No wonder that the classical community was the first to embrace CD. I know
many rockers that even today claim that analog captures the guitar sound
more accurately.
I believe the Synclavier uses a sampling frequency of 100kHz. If it needs
that much to create a specific sound, how can a lowly 44.1 kHz sampling rate
reveal the subtleties that a programmer/musician may want to play.
At any rate, to continue this discussion is fruitless for me. There are
limitations, and whether one can hear it or not is a subjective thing.
Different people are sensitive to different things, but of course your own
personal sensitivities are all that counts.


Stu

"audiodir"

I have no doubt as to the Fourier statements and theory,



** You are a mentally defective ass with no comprehension of anything.



.............. Phil

On Mon, 07 Mar 2005 08:11:00 GMT, "audiodir"
wrote:

I have no doubt as to the Fourier statements and theory, but that is also
based on unlimited data. It would seem that in the case where there is an
upper limit, then the data available becomes truncated as you approach that
limit, making recreation of a waveform much more difficult.
Perhaps the problem is not so much with the Nyquist theory as its
application. After all, a DAC has to set the parameters of what waveform it
seeks to recreate. I believe the Spectral DAC had an option to set different
algorithms to use in the decoding process. The waveforms generated are not
dissimilar to the differences seen in a cadcam system when asked to
interpolate a curve over various points.

Different situation entirely. The whole point of Nyquist/Shannon is
that, if you have only two sampled points of reference, i.e. if the
samples are of a signal having a frequency between one-half and
one-third of the sampling rate, and if you *know* that the input
signal is bandlimited to less than half the sampling frequency, then
only *one* possible curve will fit the two points - it is a sine wave
of a specific frequency and amplitude.

If the curve were *not* a sine wave, then it would *by definition*
contain harmonic content, and hence would *not* be band-limited to
less than half the sampling frequency. This causes an effect known as
aliasing, which is a *distortion* which does not exist in a properly
implemented sampling system.

It is true that the Spectral and several other DACs (also some Wadia,
Pioneer and Sony CD players), did indeed use reconstruction filters
which allowed out of band products to appear at the output. This false
imaging is a *distortion*, in other words it's a bug, not a feature.
Heck, some loonytunes 'high end' players from the like of YBA and
Audio Note, don't even *have* a reconstruction filter, they just let
*all* the rubbish out!

While most music is a series of sine waves,

Actually, *all* bandwidth-limited signals can be represented as a
series of sine waves.

there are a lot of impulses and
other unusual waveforms (think of the 'grundge' associated with rock
electric guitars and the inherent distortion those instruments can produce).

What *appear* to be impulses, certainly have finite leading edges, and
can threfore be represented by a series of sine waves - even if you
need to up the sampling rate to capture anything higher than 22kHz.
But why would you want to, unless you are a cat or a bat?

BTW, the 'grunge' associated with a heavily distorted electric guitar
is all below 10kHz, so no problems capturing it.

No wonder that the classical community was the first to embrace CD. I know
many rockers that even today claim that analog captures the guitar sound
more accurately.

People make all kinds of crazy claims - and would *you* take the word
of someone who's spent the last decade with his ears three feet from a
Marshall stack - and his nose in a snowdrift? :-)

I believe the Synclavier uses a sampling frequency of 100kHz. If it needs
that much to create a specific sound, how can a lowly 44.1 kHz sampling rate
reveal the subtleties that a programmer/musician may want to play.

Who says that the Synclavier *needs* a 100k sampling rate? With modern
kit, 24/96 sampling is trivially easy (and cheap) to do, but it's very
arguable that it's *necessary* for 'perfect sound'. You probably have
a 24/96 soundcard in your PC, but do you *need* 96k sampling?

At any rate, to continue this discussion is fruitless for me. There are
limitations, and whether one can hear it or not is a subjective thing.
Different people are sensitive to different things, but of course your own
personal sensitivities are all that counts.

And not one single person has yet been found who can reliably and
repeatably tell the difference between 44.1k and 96k sampling, when
they don't *know* which is playing.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

"audiodir" wrote in message
news0UWd.82680$uc.5110@trnddc04...
(big snip)

I believe the Synclavier uses a sampling frequency of 100kHz. If it needs
that much to create a specific sound, how can a lowly 44.1 kHz sampling
rate reveal the subtleties that a programmer/musician may want to play.

The Synclavier uses a sampling frequency if 50kHz, which was chosen
by the maker New England Digital, long before 44.1 or 44kHz came into
being.

Iain

On Mon, 7 Mar 2005 07:30:51 +0000 (UTC), Stewart Pinkerton
wrote:

On Mon, 07 Mar 2005 05:30:58 GMT, "audiodir"
wrote:

Nyquist assumes that all you want is to reproduce is a sine wave. Music is
not all sine waves.

Fourier demonstrates that *any* waveform, including music, can be
represented as a series of superimposed sinewaves. Hence, Nyquist and
Shannon are correct in their postulations. While music may not
*appear* to be sinewaves, it can be so treated for the purposes of
reproduction. Bottom line of course is that digital audio works, and
reproduces music more accurately than any other system.

no. digital is a way to create (perfect) storage and reproduction thereof due to
the fact you only need an acurate list of numbers.

but music and sound is analog, and an analog system with no D/A or A/D
converters is more accurate by rule of simplicity.

don't mistake added noise with quality of reproduction, as in the case of
scratchy vinyl!

an analog system with greater resolution will sound better then a digital
system, assuming you can hear the distortion products.

the last studio reel to reel machines that were made had a S/N of up to 120db,
far better than CD.

as for other systems, high freq. FM modulation tape systems also beat out CD.

all this techno and people run around listening to MP3s!

"Mister" = horse and cart lover

no. digital is a way to create (perfect) storage and reproduction thereof
due to
the fact you only need an acurate list of numbers.

but music and sound is analog, and an analog system with no D/A or A/D
converters is more accurate by rule of simplicity.



** Just like a horse and cart is a better mode of transport !!!!!!!!

What a colossal ****wit !!!!



don't mistake added noise with quality of reproduction, as in the case of
scratchy vinyl!


** Audible noise is bad reproduction per se.



an analog system with greater resolution will sound better then a digital
system, assuming you can hear the distortion products.



** A cart with enough horses is better that a car ??


the last studio reel to reel machines that were made had a S/N of up to
120db,
far better than CD.


** Massive, stupid lie.


as for other systems, high freq. FM modulation tape systems also beat out
CD.


** Second massive, stupid lie.

Another demented vinyl bigot for sure.




................. Phil

Mister said:

the last studio reel to reel machines that were made had a S/N of up to 120db,
far better than CD.


??????????????????

--
Sander de Waal
" SOA of a KT88? Sufficient. "

"Mister" wrote


no. digital is a way to create (perfect) storage and reproduction thereof
due to
the fact you only need an acurate list of numbers.

but music and sound is analog, and an analog system with no D/A or A/D
converters is more accurate by rule of simplicity.

don't mistake added noise with quality of reproduction, as in the case of
scratchy vinyl!



*Scratchy* Vinyl?

I hate to break into yet another mind-numbing digital/analogue debate, but
I've got to take issue with this 'scratchy' epithet that is forever being
tacked to the word 'vinyl'...

I posted these tracks:

http://www.apah69.dsl.pipex.com/show...Track%2001.mp3

http://www.apah69.dsl.pipex.com/show...Track%2002.mp3

http://www.apah69.dsl.pipex.com/show...Track%2003.mp3

for non-Usenet purposes (to demonstrate a new valve phono stage, as it
happens) - allowing for the fact they are MP3s, how scratchy (or even
'splashy') are they?

It might interest you to know that they have had no 'treatment' whatsoever
(other than trimming to length) and the deck and cart they were recorded
with are both getting on for 30 years old and cost about the same price as 2
(UK) chart CDs! (The record itself cost a whole UK quid + P&P...).

(It might please the Yanks here to know the cart is no more than an M75ED2
and quite probably still on its original stylus....!! :-)

Stewart Pinkerton wrote in
:

On Mon, 07 Mar 2005 05:30:58 GMT, "audiodir"
wrote:

Nyquist assumes that all you want is to reproduce is a sine wave. Music is
not all sine waves.

Fourier demonstrates that *any* waveform, including music, can be
represented as a series of superimposed sinewaves. Hence, Nyquist and
Shannon are correct in their postulations. While music may not
*appear* to be sinewaves, it can be so treated for the purposes of
reproduction. Bottom line of course is that digital audio works, and
reproduces music more accurately than any other system.

You are correct Stewart. I forgot about that.

r

"Stewart Pinkerton" wrote

Fourier demonstrates that *any* waveform, including music, can be
represented as a series of superimposed sinewaves. Hence, Nyquist
and
Shannon are correct in their postulations. While music may not
*appear* to be sinewaves, it can be so treated for the purposes of
reproduction. Bottom line of course is that digital audio works,
and
reproduces music more accurately than any other system.

Not including music actually, quite. Do you have a reference in
which Fourier demonstrated that *music* can be *fully* represented
as series of superimposed sinewaves?

I fear audiophools have made up their own meaning of "transient" but
I'll ask anyway: what about transients?

cheers, Ian

On Thu, 10 Mar 2005 07:13:48 GMT, "Ian Iveson"
wrote:

"Stewart Pinkerton" wrote

Fourier demonstrates that *any* waveform, including music, can be
represented as a series of superimposed sinewaves. Hence, Nyquist
and
Shannon are correct in their postulations. While music may not
*appear* to be sinewaves, it can be so treated for the purposes of
reproduction. Bottom line of course is that digital audio works,
and
reproduces music more accurately than any other system.

Not including music actually, quite. Do you have a reference in
which Fourier demonstrated that *music* can be *fully* represented
as series of superimposed sinewaves?

Which part of '*any* waveform' did you fail to understand?

I fear audiophools have made up their own meaning of "transient" but
I'll ask anyway: what about transients?

If contained within the required fs/2 bandwidth, they will be
correctly captured, as will all other waveforms. Bottom line of course
is that digital audio works, and reproduces music more accurately
than any other system.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

audiodir wrote:

Nyquist assumes that all you want is to reproduce is a sine wave. Music is
not all sine waves.

But I thought is was a plethera of combined sine waves,
many with varying amplitude, phase, and frequency.
In fact music resembles noise, but music's content
has most of its frequencies related numerically...

Music by Heavy Metal is very little different to pink noise I use to test
equipment.

A Motzart concetto is quite a lot different to noise.

All have lotsa sine waves.


Patrick Turner.



Stu

"Phil Allison" wrote in message
...

"tubesforall" = a deranged liar


Nyquist theorem states that a non-variant signal freqency can be
reproduced that is 1/2 the sample rate.


** WRONG !!!!

It says that ANY signal with frequency components not exceeding a certain
bandwidth can be *exactly* reproduced by sampling it at a rate of double
that bandwidth.

since you have gone on a tirade, you should be a bit more careful.

it says you need to sample it at MORE than double. double exactly is not
enough.

randy

"xrongor" = pedantic jerk off

"Phil Allison

"tubesforall" = a deranged liar


Nyquist theorem states that a non-variant signal freqency can be
reproduced that is 1/2 the sample rate.


** WRONG !!!!

It says that ANY signal with frequency components not exceeding a certain
bandwidth can be *exactly* reproduced by sampling it at a rate of double
that bandwidth.

since you have gone on a tirade,


** **** you - asshole.


you should be a bit more careful.


** So should have your parents, boy have they paid for their mistake.


it says you need to sample it at MORE than double.


** It must not be less than double the highest signal frequency - but can
be made arbitrarily close to double.

Your point is as worthless as you are.




.............. Phil

On Sun, 6 Mar 2005 20:31:24 -0800, "tubesforall"
wrote:

Nyquist theorem states that a non-variant signal freqency can be reproduced
that is 1/2 the sample rate.

No, it actually says *less* than half the sample rate.

Unfortunately, music that is invariant is not
terribly interesting. Thus, the common wisdom that 44.1KHz sampling can
reproduce 22 KHz music is not true.

Yes. it is.

A seminal paper from MIT shows that distortion related to sampling must
consider both the sample rate and the target word size. For today's
CDs--that is 16 bits. Thus, according to this paper, a minimum of 8X
frequency is required--10X is better. Working backwards, that means that CD
technology can only reproduce, at best, 5.5 KHz before distortion starts to
enter in. This is independant of the construction of filters and assumes a
boxcar filter (impossible in real life.)

Please cite the papar, as this is contrary to current theory - and
more importantly, to current measurements, which demonstrate that
44.1k sampling is adequate for *perfect* capture of any waveform
within a 22kHz bandwidth

Other solutions have worked hard to reduce this problem by oversampling,
adding bits, etc. All these solutions smooth the distortion created by the
original system, but they can not add information back in that is lost.
What they can do is create better sounding music by smoothing out the
jaggies in the distortion.

There is *no* distortion. Cite the paper, or cite *any* measurements
which can demonstrate such distortion. Otherwise go away, troll.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

A seminal paper from MIT shows that distortion related to sampling
must
consider both the sample rate and the target word size. For today's
CDs--that is 16 bits. Thus, according to this paper, a minimum of 8X

frequency is required--10X is better. Working backwards, that means
that CD
technology can only reproduce, at best, 5.5 KHz before distortion
starts to
enter in. This is independant of the construction of filters and
assumes a
boxcar filter (impossible in real life.)


Please cite the papar, as this is contrary to current theory - and
more importantly, to current measurements, which demonstrate that
44.1k sampling is adequate for *perfect* capture of any waveform
within a 22kHz bandwidth


Other solutions have worked hard to reduce this problem by
oversampling,
adding bits, etc. All these solutions smooth the distortion created
by the
original system, but they can not add information back in that is
lost.
What they can do is create better sounding music by smoothing out the

jaggies in the distortion.


There is *no* distortion. Cite the paper, or cite *any* measurements
which can demonstrate such distortion. Otherwise go away, troll.
--

Although the OP is tangled up in his own underwear, I think that he's
alluding to the relationship between sampling rate and quantization
noise.

Joe

In article .com,
"Joseph Meditz" wrote:

Although the OP is tangled up in his own underwear, I think that he's
alluding to the relationship between sampling rate and quantization
noise.

Can you explain the "relationship between sampling rate and quantization
noise"? I thought sampling and quantization were two independent effects,
sampling being an essentially analog effect creating no noise within the
signal bandwidth as long as the sampling rate is greater than two times
the signal bandwidth, while quantization is the conversion of sample
values to discrete digital values and does create noise?


Regards,

John Byrns


Surf my web pages at, http://users.rcn.com/jbyrns/

"Joseph Meditz" wrote:
Although the OP is tangled up in his own underwear, I think that
he's
alluding to the relationship between sampling rate and quantization
noise.

Can you explain the "relationship between sampling rate and
quantization
noise"? I thought sampling and quantization were two independent
effects,
sampling being an essentially analog effect creating no noise within
the
signal bandwidth as long as the sampling rate is greater than two
times
the signal bandwidth, while quantization is the conversion of sample
values to discrete digital values and does create noise?

The sampling theorem does not mention quantization noise. It assumes
that your samples are analog, i.e., infinite precision, snapshots of
the voltage waveform and that the reconstruction filter, which connects
the dots as it were, is also ideal. In a practical system samples are
quantized to some finite precision and the reconstruction filter is not
ideal.

If you had two identical systems each using 16 bit words but differing
only in sampling rate, one being Fs = 44.1kHz and the other with Fs =
88.2 kHz, and you sampled program material using both and then played
it on two systems that used Fs = 44.1 and 88.2 kHz respectively, then
the signal to quantization noise of the second would be 3 dB, or 1/2
bit, better than the first.

Joe

On 7 Mar 2005 12:48:24 -0800, "Joseph Meditz"
wrote:

"Joseph Meditz" wrote:
Although the OP is tangled up in his own underwear, I think that
he's
alluding to the relationship between sampling rate and quantization
noise.

Can you explain the "relationship between sampling rate and
quantization
noise"? I thought sampling and quantization were two independent
effects,
sampling being an essentially analog effect creating no noise within
the
signal bandwidth as long as the sampling rate is greater than two
times
the signal bandwidth, while quantization is the conversion of sample
values to discrete digital values and does create noise?

The sampling theorem does not mention quantization noise. It assumes
that your samples are analog, i.e., infinite precision, snapshots of
the voltage waveform and that the reconstruction filter, which connects
the dots as it were, is also ideal. In a practical system samples are
quantized to some finite precision and the reconstruction filter is not
ideal.

If you had two identical systems each using 16 bit words but differing
only in sampling rate, one being Fs = 44.1kHz and the other with Fs =
88.2 kHz, and you sampled program material using both and then played
it on two systems that used Fs = 44.1 and 88.2 kHz respectively, then
the signal to quantization noise of the second would be 3 dB, or 1/2
bit, better than the first.

Ah, I see what you're getting at. This is true, but occurs at such a
low level as to be sonically insignificant. Certainly, no one has
demonstrated an ability to hear this effect.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

On Mon, 07 Mar 2005 13:32:36 -0600, (John Byrns) wrote:

In article .com,
"Joseph Meditz" wrote:

Although the OP is tangled up in his own underwear, I think that he's
alluding to the relationship between sampling rate and quantization
noise.

Can you explain the "relationship between sampling rate and quantization
noise"? I thought sampling and quantization were two independent effects,
sampling being an essentially analog effect creating no noise within the
signal bandwidth as long as the sampling rate is greater than two times
the signal bandwidth, while quantization is the conversion of sample
values to discrete digital values and does create noise?

Another way to say what Joseph means is that finite quantization
introduces what are effectively timing errors ("jitter") in the
complete A/D/A conversion.

In the A/D/A worlds, noise and distortion are *not* different things.
And neither are amplitude and frequency modulation distortions. (Or
course, they weren't in the old analog world either; we just didn't
talk about it that way).

Digital storage is theoretically perfect after being bandwidth
limited, dynamic range limited, and quantized-and-back monotonically.
Discussion really ought to be targeted at the limitations, IMO.

Chris Hornbeck
"Say! One of you guys know how to Madison?"
-Brad in _The Rocky Horror Picture Show_

On Tue, 08 Mar 2005 02:55:13 GMT, Chris Hornbeck
wrote:

On Mon, 07 Mar 2005 13:32:36 -0600, (John Byrns) wrote:

In article .com,
"Joseph Meditz" wrote:

Although the OP is tangled up in his own underwear, I think that he's
alluding to the relationship between sampling rate and quantization
noise.

Can you explain the "relationship between sampling rate and quantization
noise"? I thought sampling and quantization were two independent effects,
sampling being an essentially analog effect creating no noise within the
signal bandwidth as long as the sampling rate is greater than two times
the signal bandwidth, while quantization is the conversion of sample
values to discrete digital values and does create noise?

Another way to say what Joseph means is that finite quantization
introduces what are effectively timing errors ("jitter") in the
complete A/D/A conversion.

While this is true, it's happening at more than 90dB below peak level.
I'm not aware of anyone having demonstrated an ability to hear the
difference among various sample rates, given a common signal
band-limited to the requirements of the lowest sampling rate, i.e. the
20kHz which is commonly taken to be the limit of human hearing.

In the A/D/A worlds, noise and distortion are *not* different things.
And neither are amplitude and frequency modulation distortions. (Or
course, they weren't in the old analog world either; we just didn't
talk about it that way).

Digital storage is theoretically perfect after being bandwidth
limited, dynamic range limited, and quantized-and-back monotonically.
Discussion really ought to be targeted at the limitations, IMO.

Indeed, and these limits are *way* below the limits of any analogue
system, indeed they're below the noise floor of most tube amps!
--

Stewart Pinkerton | Music is Art - Audio is Engineering

On 7 Mar 2005 10:56:21 -0800, "Joseph Meditz"
wrote:

Although the OP is tangled up in his own underwear, I think that he's
alluding to the relationship between sampling rate and quantization
noise.

That would still imply significant tangling, since there exists no
such relationship. Quantisation noise as a signal-correlated artifact
is completely removed by the correct use of around 1/2 LSB of dither.
This has nothing to do with sample rate.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

In article , Stewart Pinkerton
wrote:

On 7 Mar 2005 10:56:21 -0800, "Joseph Meditz"
wrote:

Although the OP is tangled up in his own underwear, I think that he's
alluding to the relationship between sampling rate and quantization
noise.

That would still imply significant tangling, since there exists no
such relationship. Quantisation noise as a signal-correlated artifact
is completely removed by the correct use of around 1/2 LSB of dither.
This has nothing to do with sample rate.

I wonder if the fact that sampling rate can be traded for quantization
levels by techniques such as noise shaping might be what has Joseph and
the others getting all "tangled up in their underwear"?


Regards,

John Byrns


Surf my web pages at, http://users.rcn.com/jbyrns/

"tubesforall" wrote in message
...
Working backwards, that means that CD
technology can only reproduce, at best, 5.5 KHz before distortion starts
to
enter in. This is independant of the construction of filters and assumes
a
boxcar filter (impossible in real life.)

Astounding theoretical work, sir! It really makes me question how a CD, let
alone a 128k MP3 can still sound good. Or maybe the theory itself is pot.
Whichever...

Tim

--
"California is the breakfast state: fruits, nuts and flakes."
Website: http://webpages.charter.net/dawill/tmoranwms

tubesforall wrote:
Nyquist theorem states that a non-variant signal freqency can be reproduced
that is 1/2 the sample rate. Unfortunately, music that is invariant is not
terribly interesting. Thus, the common wisdom that 44.1KHz sampling can
reproduce 22 KHz music is not true.

The problem is the phasing of the signal vs the sampling clock.
If the phase of the 22.05KHz tone happens to be in a phase that
creates samples of 0, max +, 0, max -, 0, etc, and then you shift
the phase by 45 degrees you'll get samples 0.707max -, 0.707 max +,
0.707max +, 0.707 max -, 0.707 max -, etc. The amplitude, if
looked at on a scope, will look lower for the second case vs the
first. However, a good reconstruction filter should fix this.
A filter designed to "ring" to "anticipate" the missing peaks
of the 22KHz wave. True, it would get a 22.05KHz square wave
wrong, but square waves have harmonics that cannot pass thru
the Nyquest theory at the ADC used to make the CD in the first
place. And human ears can't hear them anyway, so there's no
point to keep them. A lower frequency square wave does come
out as a square wave, and the reconstruction filter does not
make it into a sine wave. The reconstruction filter can be
done in the digital domain at some oversampled clock rate,
like 8X. And use deeper words to avoid truncation errors.
Then run the output of that thru a DAC running
at 8X clock rate, and use a simple low pass to get rid of
clock crud, and the audio signal will look to be reconstructed.
Distortion products from Nyquest fall outside of human
hearing, and thus not an issue.

At the ADC connected to a mic in the recording studio,
you need a brick wall low pass filter at 22KHz. Or
else that violin will violate Nyquest as its audio spectrum
most likely goes from audible to supersonic. The supersonic
stuff will alias ("fold down") into audible crud when the
CD is played back. Oversampling at the ADC and then LPF
the signal in the digital domain works well, assuming you have
a really good and deep ADC, say 24 bits at 8X.
Remastering analog master tapes also requires care to avoid
aliasing supersonic tape noise and such.



Other solutions have worked hard to reduce this problem by oversampling,
adding bits, etc. All these solutions smooth the distortion created by the
original system, but they can not add information back in that is lost.

But nobody will miss that info, so you need not preserve it.

What they can do is create better sounding music by smoothing out the
jaggies in the distortion.

The jaggies are supersonic anyway, so they are filtered out
(to avoid intermod problems in the user's audio amp system).