In the current thread "Report - 2005 London HiFi Show", Andy Evans
talks about digital audio as the wave of the future, and Patrick too
mentioned it twice already.

Can someone please explain to me what digital audio is? I haven't read
the trade magazines in a decade, so I am right out of it; please start
from scratch and don't deprive me of any riches. Is it audio made by
noughts and ones; does the entire chain to and including the speaker
become digital? I thought part of even the most rabid tubie's audio
chain was digital already, in that a CD player is a digital on-off
device as far as the laser that reads it is concerned.

TIA.

Andre Jute

On 23 Sep 2005 21:43:31 -0700, "Andre Jute" wrote:

Can someone please explain to me what digital audio is?

Digital portions of audio equipment work with integer
numbers; analog portions work with real numbers.

Good fortune,

Chris Hornbeck

On Sat, 24 Sep 2005 14:16:24 GMT, Chris Hornbeck
wrote:

On 23 Sep 2005 21:43:31 -0700, "Andre Jute" wrote:

Can someone please explain to me what digital audio is?

Digital portions of audio equipment work with integer
numbers; analog portions work with real numbers.

A transparent lie, since analogue audio doesn't work with any kind of
numbers. However, since digital audio uses numbers so large that they
greatly exceed the resolution of any known analogue system, this isn't
actually a problem.

Basically, digital audio samples the incoming analogue signal many
tens of thousands of times a second, and takes a 'snapshot' of the
signal amplitude at that exact moment in time. These snapshots are
stored as digital data, and are then fed (by various means which are
irrelevant to the basic process) to a device which reconstructs the
millions of snapshots into an analogue signal once more. The important
thing is that the intervening digital process is *much* more able to
provide an exact equivalent of the original analogue input signal,
than is analogue tape or especially vinyl.

Being a digital data stream like any other compuer data, it is of
course also capable of being copied hundreds of times with *zero*
genertation loss, again very unlike analogue, which goes though at
least least six intermediate stages from microphone to speaker, with
losses at each stage.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

On Sat, 24 Sep 2005 14:40:08 +0000 (UTC), Stewart Pinkerton
wrote:

Can someone please explain to me what digital audio is?

Digital portions of audio equipment work with integer
numbers; analog portions work with real numbers.

A transparent lie, since analogue audio doesn't work with any kind of
numbers. However, since digital audio uses numbers so large that they
greatly exceed the resolution of any known analogue system, this isn't
actually a problem.

I thought this would be more apparent than it seems
to be. Analog values (voltage, pressure, whatever)
are within the set of real numbers. Digital values
are within the integer number set.

Didn't mean to say that your baby was ugly, just
answering the question. There's no moral value to
number sets. Both, by the way, are infinite.

Good fortune,

Chris Hornbeck

On Sat, 24 Sep 2005 15:13:19 GMT, Chris Hornbeck
wrote:

On Sat, 24 Sep 2005 14:40:08 +0000 (UTC), Stewart Pinkerton
wrote:

Can someone please explain to me what digital audio is?

Digital portions of audio equipment work with integer
numbers; analog portions work with real numbers.

A transparent lie, since analogue audio doesn't work with any kind of
numbers. However, since digital audio uses numbers so large that they
greatly exceed the resolution of any known analogue system, this isn't
actually a problem.

I thought this would be more apparent than it seems
to be. Analog values (voltage, pressure, whatever)
are within the set of real numbers. Digital values
are within the integer number set.

Didn't mean to say that your baby was ugly, just
answering the question. There's no moral value to
number sets. Both, by the way, are infinite.

Nice try, but still an attempt to trot out the old 'analogue has
infinite resolution' ********.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

"Stewart Pinkerton" wrote in message
...
: On Sat, 24 Sep 2005 15:13:19 GMT, Chris Hornbeck
: wrote:

: Nice try, but still an attempt to trot out the old 'analogue has
: infinite resolution' ********.
: --
:
: Stewart Pinkerton | Music is Art - Audio is Engineering

...since you brought it up:
what *is* the resolution of analog, would you be wanting to claim ?
R.

On Sat, 24 Sep 2005 17:25:28 +0000 (UTC), Stewart Pinkerton
wrote:

I thought this would be more apparent than it seems
to be. Analog values (voltage, pressure, whatever)
are within the set of real numbers. Digital values
are within the integer number set.

Didn't mean to say that your baby was ugly, just
answering the question. There's no moral value to
number sets. Both, by the way, are infinite.

Nice try, but still an attempt to trot out the old 'analogue has
infinite resolution' ********.

OK, whatever you say. So what is your definition of
the difference between analog and digital?

Chris Hornbeck

"Stewart Pinkerton" wrote in message
...
On Sat, 24 Sep 2005 15:13:19 GMT, Chris Hornbeck
wrote:

On Sat, 24 Sep 2005 14:40:08 +0000 (UTC), Stewart Pinkerton
wrote:

Can someone please explain to me what digital audio is?

Digital portions of audio equipment work with integer
numbers; analog portions work with real numbers.

A transparent lie, since analogue audio doesn't work with any kind of
numbers. However, since digital audio uses numbers so large that they
greatly exceed the resolution of any known analogue system, this isn't
actually a problem.

I thought this would be more apparent than it seems
to be. Analog values (voltage, pressure, whatever)
are within the set of real numbers. Digital values
are within the integer number set.

Didn't mean to say that your baby was ugly, just
answering the question. There's no moral value to
number sets. Both, by the way, are infinite.

Nice try, but still an attempt to trot out the old 'analogue has
infinite resolution' ********.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

Perhaps Stewart. There is an article in the recently released "AudioXpress"
magazine about this very topic. BTW: Did you know that you have an article
in that very same issue? John, I've read most of your magazine articles and
I don't mean to embarrass you, but it's an honor & privilege to have you
associated with this NG. Keep up the very fine work.
west

Yes, but integers belong to the infinite set called "Aleph Null" (or the
countable infinity) while real numbers belong to a set of greater infinity.
As of yet there is no metric for determining the exact difference--only that
there is at least one infinity order greater than Aleph Null. This was
first proved rigorouly (as far as we know) by George Cantor in the 19th
century. The proof known as the "Cantor Ternary Set Method" is a standard
problem for upper level Real Variable Analysis students on the PhD math or
phsics track Cantor is also called the father of Set Theory--which led to
logical inconsistancies that were only dealt with rigorously by Einstien's
friend Max Godel.

Thus, mathematically speaking, the digital domain is far less exact than the
analog domain.

Of course, the real level of exactness is determnined in the digital domain
by the rate of sampling and in the analog domain by the maximum frequency
content of the sample stored. 24 bit 196KHz sampling in the studio has a
theoretical Nyquist limit equal to approximately the analog content stored
in the best technologies--about 100HKz. Of course the digital domain has
the further problem true undistorted content for non-steady state signals
(which is required for the infinite filters in the Nyquist limit) that
limits the pure mathematical content--undistorted--to about 50 KHz at 24
bits and 20KHz at 16 bit in the studio example above.

Didn't mean to say that your baby was ugly, just
answering the question. There's no moral value to
number sets. Both, by the way, are infinite.

Good fortune,

Chris Hornbeck

On Sat, 24 Sep 2005 23:32:35 +0200, "Ruud Broens"
wrote:

"Stewart Pinkerton" wrote in message
.. .
: On Sat, 24 Sep 2005 15:13:19 GMT, Chris Hornbeck
: wrote:

: Nice try, but still an attempt to trot out the old 'analogue has
: infinite resolution' ********.

..since you brought it up:
what *is* the resolution of analog, would you be wanting to claim ?

Standard definition - it's the smallest unique amplitude which can be
reliably detected above the wideband noise floor.

That in itself is not of much use in an audio context without knowing
the available peak signal in the same device, i.e. the dynamic range,
normally quoted in deciBels. Nowadays, the simplest shorthand is to
refer to that dynamic range in terms of its equivalent bit depth, e.g.
the very best vinyl has about 12 bits dynamic range (72dB), while the
very widest ranging music master tapes have less than 14 bit
equivalent range (84dB). CD of course has about 15.5 bits or 93dB, not
the full 16 bits due to about 1/2 LSB dither being applied to
decorrelate the noise floor from the sampling rate.

Before anyone starts rabbiting on about 'hearing below the noise
floor', this extends the available dynamic range by 10-15dB and is
achieved by narrowing the bandwidth of the noise floor to match the
narrow-band nature of our aural receptors. It should be noted that
this effect appllies to digital audio in exactly the same way that it
applies to analogue.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

On Sat, 24 Sep 2005 23:46:29 GMT, Chris Hornbeck
wrote:

On Sat, 24 Sep 2005 17:25:28 +0000 (UTC), Stewart Pinkerton
wrote:

I thought this would be more apparent than it seems
to be. Analog values (voltage, pressure, whatever)
are within the set of real numbers. Digital values
are within the integer number set.

Didn't mean to say that your baby was ugly, just
answering the question. There's no moral value to
number sets. Both, by the way, are infinite.

Nice try, but still an attempt to trot out the old 'analogue has
infinite resolution' ********.

OK, whatever you say. So what is your definition of
the difference between analog and digital?

In principle, there isn't one. In practice, digital audio suffers no
generation loss (very important when you consider all the intermediate
storage stages between the signal leaving the microphone and arriving
at your loudspeakers), it has no problems with full-level signals
anywhere within its frequency range, it has vanishingly nlow
distortion at all frequencies and at all signal levels, and it has
much wider dynamic range than any analogue system.

A digital audio system, and particularly when we look at the
ubiquitous 24/96 studio standard which applies all the way up to the
final mixdown master for CD (or even beyond on DVD), is in practice
limited only by the analogue parts of the system. The digital side is
utterly transparent. Of course, some people just can't let go of that
warm cuddly feeling, so you do get people asking for their
immaculately clean digital masters to be given a final pass through an
analogue tape machine to reintroduce that distortion and poise that
they've been used to all these previous years.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

On Sun, 25 Sep 2005 00:38:41 GMT, "west"
wrote:

"Stewart Pinkerton" wrote in message
.. .
On Sat, 24 Sep 2005 15:13:19 GMT, Chris Hornbeck
wrote:

On Sat, 24 Sep 2005 14:40:08 +0000 (UTC), Stewart Pinkerton
wrote:

Can someone please explain to me what digital audio is?

Digital portions of audio equipment work with integer
numbers; analog portions work with real numbers.

A transparent lie, since analogue audio doesn't work with any kind of
numbers. However, since digital audio uses numbers so large that they
greatly exceed the resolution of any known analogue system, this isn't
actually a problem.

I thought this would be more apparent than it seems
to be. Analog values (voltage, pressure, whatever)
are within the set of real numbers. Digital values
are within the integer number set.

Didn't mean to say that your baby was ugly, just
answering the question. There's no moral value to
number sets. Both, by the way, are infinite.

Nice try, but still an attempt to trot out the old 'analogue has
infinite resolution' ********.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

Perhaps Stewart. There is an article in the recently released "AudioXpress"
magazine about this very topic.

Indeed so, and I expect modern high-speed Class D amplifiers to spread
across the home audio world at great speed. They're already used in
some 'high end' designs such as the (now pretty obsolete) Tact
Millenium mentioned in the article, and of course are at the heart of
the superb B&O Lab 5 speakers. B&O making truly high end speakers -
who'd have thought it? :-)

BTW: Did you know that you have an article
in that very same issue?

You may be confusing me with someone else.

John, I've read most of your magazine articles and
I don't mean to embarrass you, but it's an honor & privilege to have you
associated with this NG. Keep up the very fine work.
west


--

Stewart Pinkerton | Music is Art - Audio is Engineering

"Stewart Pinkerton" wrote in message
news : On Sat, 24 Sep 2005 23:46:29 GMT, Chris Hornbeck
: wrote:
:
: On Sat, 24 Sep 2005 17:25:28 +0000 (UTC), Stewart Pinkerton
: wrote:
:
: I thought this would be more apparent than it seems
: to be. Analog values (voltage, pressure, whatever)
: are within the set of real numbers. Digital values
: are within the integer number set.
:
: Didn't mean to say that your baby was ugly, just
: answering the question. There's no moral value to
: number sets. Both, by the way, are infinite.
:
: Nice try, but still an attempt to trot out the old 'analogue has
: infinite resolution' ********.
:
: OK, whatever you say. So what is your definition of
: the difference between analog and digital?
:
: In principle, there isn't one. In practice, digital audio suffers no
: generation loss (very important when you consider all the intermediate
: storage stages between the signal leaving the microphone and arriving
: at your loudspeakers), it has no problems with full-level signals
: anywhere within its frequency range, it has vanishingly nlow
: distortion at all frequencies and at all signal levels, and it has
: much wider dynamic range than any analogue system.
:
: A digital audio system, and particularly when we look at the
: ubiquitous 24/96 studio standard which applies all the way up to the
: final mixdown master for CD (or even beyond on DVD), is in practice
: limited only by the analogue parts of the system. The digital side is
: utterly transparent. Of course, some people just can't let go of that
: warm cuddly feeling, so you do get people asking for their
: immaculately clean digital masters to be given a final pass through an
: analogue tape machine to reintroduce that distortion and poise that
: they've been used to all these previous years.
: --
:
: Stewart Pinkerton | Music is Art - Audio is Engineering

That's all fine 'n dandy, Stewart,
but let's see if what you give as a response makes sense:

Analog values (voltage, pressure, whatever)
are within the set of real numbers. Digital values
are within the integer number set.--
Nice try, but still an attempt to trot out the old 'analogue has
infinite resolution' ********
yeah, great rebuttal, there :-) noted

So what is your definition of
the difference between analog and digital?--
In principle, there isn't one.

youse call *that* definition, scott-side ?

straw man about digital recording and producing
having nada, zip, nonwhatso-ever to do with
the analogue digital difference, just a
summation of an implementation
and the nicceties we can do with 'm,
noted.

Rudy

"vinylbigot" = a grossly autistic menace


(snip pseudo mathematical drivel)


Thus, mathematically speaking, the digital domain is far less exact than
the analog domain.


** A complete irrelevance even - if it were true.


Of course, the real level of exactness is determnined in the digital
domain by the rate of sampling and in the analog domain by the maximum
frequency content of the sample stored.


** Wrong on both counts.

Frequency is only one element of an audio signal.


24 bit 196KHz sampling in the studio has a theoretical Nyquist limit
equal to approximately the analog content stored in the best
technologies--about 100HKz.


** More asinine drivel best technologies = what ??

A wiggly channel scraped into a piece of plastic ???


( snip even more stomach churning crapology)


Puke, puke .....



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

On Sat, 24 Sep 2005 22:38:02 -0700, "vinylbigot"
wrote:

Yes, but integers belong to the infinite set called "Aleph Null" (or the
countable infinity) while real numbers belong to a set of greater infinity.
As of yet there is no metric for determining the exact difference--only that
there is at least one infinity order greater than Aleph Null. This was
first proved rigorouly (as far as we know) by George Cantor in the 19th
century. The proof known as the "Cantor Ternary Set Method" is a standard
problem for upper level Real Variable Analysis students on the PhD math or
phsics track Cantor is also called the father of Set Theory--which led to
logical inconsistancies that were only dealt with rigorously by Einstien's
friend Max Godel.

Thus, mathematically speaking, the digital domain is far less exact than the
analog domain.

Only once you get infinitely far from reality.............

Of course, the real level of exactness is determnined in the digital domain
by the rate of sampling and in the analog domain by the maximum frequency
content of the sample stored.

Utter (and ignorant) rubbish, as one might expect from a vinyl bigot.

Exactness is a measure of amplitude, not of frequency. The
*information content* is of course a function of both dynamic range
*and* bandwidth. Frequency range alone is perhaps the least important
aspect of the comparison.

24 bit 196KHz sampling in the studio has a
theoretical Nyquist limit equal to approximately the analog content stored
in the best technologies--about 100HKz.

It's 192k, and the Nyquist limit is just below 96kHz. Furthermore,
regardless of the 50kHz or so bandwidth of 30ips studio master tapes
(although not the commonly used large capsule condenser microphones,
of course.......), nothing above 20kHz or so makes it onto vinyl
anyway, and almost averything above 15kHz is just noise.

Of course the digital domain has
the further problem true undistorted content for non-steady state signals
(which is required for the infinite filters in the Nyquist limit) that
limits the pure mathematical content--undistorted--to about 50 KHz at 24
bits and 20KHz at 16 bit in the studio example above.

More ignorant rubbish - the bit depth has nothing whatever to do with
the frequency range. Further, modern systems are beautifully linear up
to more than 90kHz for 192k sampling, and close to 21kHz for 44.1k
sampling. Vinyl of course rolls off above 12-15kHz and below 40Hz, so
there really is no comparison at all in the real world.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

On Sat, 24 Sep 2005 22:38:02 -0700, "vinylbigot"
wrote:

Thus, mathematically speaking, the digital domain is far less exact than the
analog domain.

Of course, the real level of exactness is determnined in the digital domain
by the rate of sampling and in the analog domain by the maximum frequency
content of the sample stored. 24 bit 196KHz sampling in the studio has a
theoretical Nyquist limit equal to approximately the analog content stored
in the best technologies--about 100HKz. Of course the digital domain has
the further problem true undistorted content for non-steady state signals
(which is required for the infinite filters in the Nyquist limit) that
limits the pure mathematical content--undistorted--to about 50 KHz at 24
bits and 20KHz at 16 bit in the studio example above.

There are several conceptual errors above. The most obvious
is that the level of "exactness" in analog or digital storage
is limited by the number set used; ain't true 'cause ain't
relevant.

The more subtle, because seemingly intuitive, is that
distortion increases as the Nyquist limit is approached.
This idea arises in the same way that the idea of
"stairsteps" in digital storage arises. And is equally
incorrect.

An idealized A/D/A conversion, meaning including dither,
produces a *perfect* reproduction of the original
anti-alias-filtered original, plus a small random
noise component.

And, incidentally, the oft-expressed and oft-assumed
idea that distortion increases at lower signal levels
in an idealized A/D/A conversion is also incorrect.


Regarding "resolution", the only useful definition in
a monotonic system is the same as signal-to-noise
ratio. True monotonicity is rare and difficult in the
real world, but we're still talking theory here.

Good fortune,

Chris Hornbeck

On Sun, 25 Sep 2005 07:05:58 +0000 (UTC), Stewart Pinkerton
wrote:

So what is your definition of
the difference between analog and digital?

In principle, there isn't one.

I'd be interested in exploring this if you are.
Sounds intriguing, if not provacative,

Where to begin?

Thanks for (finally!) an interesting topic,

Chris Hornbeck

Good points. I agree with your comment on number sets. Neither are
relevant to music. I was just noting that a pure and unrestrained analog
number set (real numbers) is more exact than integer representation as
proved by infinite theory. Of course, the infinitude of the integer set far
exceeds our capability to reproduce so the point is moot.

Also agree with dynamics not affecting distortion--again this is directly
visible in the theory.

However, there is a disagreement about what constitutes distortion related
to frequency in the case where infinite IIR filters are not used (as in
today's audio) and/or where the transient signal does not always extend to
the boundaries of the filter interval--even if the filter is theoretically
perfect. What is verifiably true is that higher sampling at the time of
recording produces better sounding music--I've not found anyone who
disagrees with that in a blind A/B listening test. Sony labs also came to
the same conclusion which is one of the reasons the Super Audio CD
technology was introduced. If if were true that 44.1KHz sampling produced
the complete undistorted orginal signal bandpass limited to 22KHz, why does
SACD sound better?

I'll try to find the MIT article that deals with this and post a link to it.
Also, there are a number of AES papers on this topic, but those are not free
to be posted.

"Chris Hornbeck" wrote in message
...
On Sat, 24 Sep 2005 22:38:02 -0700, "vinylbigot"
wrote:

Thus, mathematically speaking, the digital domain is far less exact than
the
analog domain.

Of course, the real level of exactness is determnined in the digital
domain
by the rate of sampling and in the analog domain by the maximum frequency
content of the sample stored. 24 bit 196KHz sampling in the studio has a
theoretical Nyquist limit equal to approximately the analog content stored
in the best technologies--about 100HKz. Of course the digital domain has
the further problem true undistorted content for non-steady state signals
(which is required for the infinite filters in the Nyquist limit) that
limits the pure mathematical content--undistorted--to about 50 KHz at 24
bits and 20KHz at 16 bit in the studio example above.

There are several conceptual errors above. The most obvious
is that the level of "exactness" in analog or digital storage
is limited by the number set used; ain't true 'cause ain't
relevant.

The more subtle, because seemingly intuitive, is that
distortion increases as the Nyquist limit is approached.
This idea arises in the same way that the idea of
"stairsteps" in digital storage arises. And is equally
incorrect.

An idealized A/D/A conversion, meaning including dither,
produces a *perfect* reproduction of the original
anti-alias-filtered original, plus a small random
noise component.

And, incidentally, the oft-expressed and oft-assumed
idea that distortion increases at lower signal levels
in an idealized A/D/A conversion is also incorrect.


Regarding "resolution", the only useful definition in
a monotonic system is the same as signal-to-noise
ratio. True monotonicity is rare and difficult in the
real world, but we're still talking theory here.

Good fortune,

Chris Hornbeck

On Wed, 28 Sep 2005 16:15:15 -0700, "vinylbigot"
wrote:

Good points. I agree with your comment on number sets. Neither are
relevant to music. I was just noting that a pure and unrestrained analog
number set (real numbers) is more exact than integer representation as
proved by infinite theory.

WTF is "infinite theory"? The above is incorrect in several
interpretations.

However, there is a disagreement about what constitutes distortion related
to frequency in the case where infinite IIR filters are not used (as in
today's audio) and/or where the transient signal does not always extend to
the boundaries of the filter interval--even if the filter is theoretically
perfect. What is verifiably true is that higher sampling at the time of
recording produces better sounding music--I've not found anyone who
disagrees with that in a blind A/B listening test. Sony labs also came to
the same conclusion which is one of the reasons the Super Audio CD
technology was introduced. If if were true that 44.1KHz sampling produced
the complete undistorted orginal signal bandpass limited to 22KHz, why does
SACD sound better?

For a better perspective on this issue, I'd suggest
the various threads that have run in rec.audio.pro .
"Verifiably true" is a big word, and SACD is apparently
an apples and oranges issue. In these early days of
an exploration, it's especially important to maintain
a proper scepticism.


I'll try to find the MIT article that deals with this and post a link to it.
Also, there are a number of AES papers on this topic, but those are not free
to be posted.

Thanks! Please don't feel that I'm coming down on you
or have some agenda. Actually, I have more than fifty
feet of vinyl and a Keith Monks record cleaner here at
the shack, still in use. But there are so many seemingly
intuitive but actually incorrect ideas floating around
that I try to patch up the ones that I can.

Good fortune,

Chris Hornbeck
"I had a perspective on the booing, too. You
can kill somebody with kindness." -Bob Dylan

"vinylbigot"

If if were true that 44.1KHz sampling produced the complete undistorted
orginal signal bandpass limited to 22KHz, why does SACD sound better?



** It doesn't .

SACD is an notorious fraud.



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

On Wed, 28 Sep 2005 16:15:15 -0700, "vinylbigot"
wrote:

Good points. I agree with your comment on number sets. Neither are
relevant to music. I was just noting that a pure and unrestrained analog
number set (real numbers) is more exact than integer representation as
proved by infinite theory. Of course, the infinitude of the integer set far
exceeds our capability to reproduce so the point is moot.

Also agree with dynamics not affecting distortion--again this is directly
visible in the theory.

However, there is a disagreement about what constitutes distortion related
to frequency in the case where infinite IIR filters are not used (as in
today's audio) and/or where the transient signal does not always extend to
the boundaries of the filter interval--even if the filter is theoretically
perfect. What is verifiably true is that higher sampling at the time of
recording produces better sounding music--I've not found anyone who
disagrees with that in a blind A/B listening test.

I've not found anyone who has actually done such a comparison. OTOH,
24/96 has pretty much become the de facto studio standard, and can be
replayed on any DVD player, so perhaps the point is moot.

Sony labs also came to
the same conclusion which is one of the reasons the Super Audio CD
technology was introduced.

Which was fatally flawed - hence the move by Sony away from DSD to the
hybrid DSD-Wide for recording, which is simply another flavour of the
high-oversampled low-bit technology now widely used in all digital
audio systems. SACD replay is simply a down-conversion of this to a
lower-resolution single-bit version.

If if were true that 44.1KHz sampling produced
the complete undistorted orginal signal bandpass limited to 22KHz, why does
SACD sound better?

That has yet to be agreed in a true blind test comparison.

--

Stewart Pinkerton | Music is Art - Audio is Engineering

"Chris Hornbeck" wrote in message
...
On Wed, 28 Sep 2005 16:15:15 -0700, "vinylbigot"
wrote:

Good points. I agree with your comment on number sets. Neither are
relevant to music. I was just noting that a pure and unrestrained analog
number set (real numbers) is more exact than integer representation as
proved by infinite theory.

WTF is "infinite theory"? The above is incorrect in several
interpretations.


The part of math theory that deals with infinite numbers--first codified by
George Cantor.

On Thu, 29 Sep 2005 17:11:07 -0700, "vinylbigot"
wrote:

WTF is "infinite theory"? The above is incorrect in several
interpretations.


The part of math theory that deals with infinite numbers--first codified by
George Cantor.

OK, so you mean something like: the infinite set of
integer numbers is a subset of the infinite set of
real numbers.

Fair enough, and true, but irrelevant.

Thanks for your thoughts,

Chris Hornbeck