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HiFi vs. Computer

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  • Speakers
  • Computers
  • Sound Cards
  • Audio
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Anonymous
May 30, 2005 12:42:07 AM

Archived from groups: rec.audio.tech (More info?)

Hi,

I'm wondering, how a good computer with a good graphic card + good
speakers can compare to a good HiFi System?

Since good soundcards can be quite expensive, and that only for the card
itself, I would suspect, that that good computer/soundcard and good
speaker combo can be as good as a good HiFi System?

So I really don't know much about these things.


Thanks for any hints.

calmar

--
calmar
(o_ It rocks: LINUX + Command-Line-Interface
//\
V_/_ http://www.calmar.ws

More about : hifi computer

Anonymous
May 30, 2005 12:42:08 AM

Archived from groups: rec.audio.tech (More info?)

"calmar" wrote ...
> I'm wondering, how a good computer with a good graphic card

The graphic card will have no effect on how the system sounds.

+ good speakers can compare to a good HiFi System?

Likely the speakers themselves will be the most critical part of
any music playback system.

> Since good soundcards can be quite expensive,

Your average-to-good sound card is likely as good as your
average CD players in "sound quality".

> and that only for the card itself, I would suspect, that that good
> computer/soundcard and good speaker combo can be as good
> as a good HiFi System?

Are you asking about just the computer as a SOURCE? Or are
you asking about your typical computer "multi-media" little
plastic speakers with built-in amplifier?

A computer as a sound SOURCE is roughly equivalent to a
consumer CD player.

Computer speakers are generally lousy to horrible compared
to average name-brand stereo speakers.
Anonymous
May 30, 2005 1:44:12 AM

Archived from groups: rec.audio.tech (More info?)

On Sun, 29 May 2005 20:42:07 +0200, calmar <calmar@calmar.ws> wrote:

>I'm wondering, how a good computer with a good graphic card + good
>speakers can compare to a good HiFi System?
>
>Since good soundcards can be quite expensive, and that only for the card
>itself, I would suspect, that that good computer/soundcard and good
>speaker combo can be as good as a good HiFi System?

For serious music use, you'd choose exactly the same amplifier and
speakers as you would for a hi-fi system. So the only difference is
the source. Computer v. stand-alone CD player or other source.

If you're playing CDs and your computer has a digital output (and your
amp has a digital input) you're just swapping one utility-standard CD
mechanism for another. No difference.

If you're playing MP3 or other format sound files, quality is down to
the quality of the file. MP3 ranges from pretty good to pretty
awful, depending on degree of compression.

If you're making an analogue link from computer to amplifier, a rather
better sound card than what is usually built in to computers is a good
idea. But this doesn't have to be expensive.

If you're into audiophile foolery, continue to believe what you want
to believe. :-)
Related resources
Anonymous
May 30, 2005 2:04:05 AM

Archived from groups: rec.audio.tech (More info?)

On 2005-05-29, calmar <calmar@calmar.ws> wrote:

Hi again,

when I'm already asking, how is the difference between:

- computer + sundcard
- mp3 player (let's say on 320kbps)
- cd player playing mp3's (e.g 320kbps)
- Hi-Fi system player those mp3's or cd

These systems connected all to the same speakers

Maybe it's possible to say some general things about these ways to play
musik quality related?

thx and cheers
calmar


--
calmar
(o_ It rocks: LINUX + Command-Line-Interface
//\
V_/_ http://www.calmar.ws
Anonymous
May 30, 2005 2:04:06 AM

Archived from groups: rec.audio.tech (More info?)

"calmar" wrote ...
> when I'm already asking, how is the difference between:
>
> - computer + sundcard
> - mp3 player (let's say on 320kbps)
> - cd player playing mp3's (e.g 320kbps)
> - Hi-Fi system player those mp3's or cd
>
> These systems connected all to the same speakers
>
> Maybe it's possible to say some general things about these
> ways to play musik quality related?

WHAT speakers? WHAT amplifier?

If you are talking about little plastic "computer speakers" they
will all sound lousy.

If you are talking about real stereo amplifier and speakers,
they will quite possibly be indistinguishable playing MP3
files. On a decent system, you should be able to hear that a
real CD sounds better than MP3. Regardless of whether it
is played on a computer or on a CD/MP3 player.

The sound will be much more affected by the speakers than
by the source (computer vs. CD/MP3 player).
Anonymous
May 30, 2005 9:39:43 AM

Archived from groups: rec.audio.tech (More info?)

calmar wrote:

> I'm wondering, how a good computer with a good graphic card + good
> speakers can compare to a good HiFi System?

If loudspeakers and amp are kept constant this is mainly about the
actual quality of the DA conversion.

> Since good soundcards can be quite expensive,

Some soundcards made for the gamers can be as costly as or costlier than
cards made for the listener.

> and that only for the card itself, I would suspect, that
> that good computer/soundcard and good speaker combo
> can be as good as a good HiFi System?

The quality of the computer doesn't really come in to this, a Pentium
"640" equipped box or a Pentium II equipped box sound the same with the
same soundcard, and if you connect the output of the sound card via a
passive attenuator (to get the coarse level matching right) to a
poweramp or to active high quality loudspeakers then it can be very
good. This however is not about the loudspeakers from the "Yonder Corner
Olde Computer Shoppe". nor about a sound card it is likely to retail.

5+1 gets to be somewhat more complicated, but the general principles
above still apply, there is no "vs." - all things equal there only is
"how good is the DA conversion", because it will end up being about
comparing DA converter, as for the rest of the reproduction most people
would be better off connecting the sound output from the computer to
their stereo anyway.

> So I really don't know much about these things.

We all have a frontier of learning, it is beyond the practical to cover
the issue completely here.

> calmar


Kind regards

Peter Larsen


*******************************************
* My site is at: http://www.muyiovatki.dk *
*******************************************
Anonymous
May 30, 2005 12:08:21 PM

Archived from groups: rec.audio.tech (More info?)

"calmar" <calmar@calmar.ws> wrote in message
news:slrnd9k37v.4ve.calmar@news.calmar.ws...
> Hi,
>
> I'm wondering, how a good computer with a good graphic card + good
> speakers can compare to a good HiFi System?
>
> Since good soundcards can be quite expensive, and that only for the card
> itself, I would suspect, that that good computer/soundcard and good
> speaker combo can be as good as a good HiFi System?
>
> So I really don't know much about these things.


Rather depends on what you are going to use fo an amplifier and speakers.


Also a computer doesn't generally look so great in the lounge, and doesn't
have a remote control.

geoff
Anonymous
May 30, 2005 12:08:22 PM

Archived from groups: rec.audio.tech (More info?)

Geoff Wood wrote:
> Also a computer doesn't generally look so great in the lounge, and doesn't
> have a remote control.

Depends on the model/accessories/software. Some are marketed as
multimedia machines, and you can get remotes as peripherals, and the
laptop I have dedicated to my stereo system is set up for remote control
via the network.

But that's offtopic for the question as asked. The real answer is: Given
a good soundcard, and given non-compressed data (or losslessly
compressed data), a PC can certainly be a "hi-fi" recording/playback system.
Anonymous
May 30, 2005 8:08:09 PM

Archived from groups: rec.audio.tech (More info?)

In article <slrnd9k37v.4ve.calmar@news.calmar.ws>, calmar@calmar.ws says...

>Hi,
>I'm wondering, how a good computer with a good graphic card + good
>speakers can compare to a good HiFi System?
>Since good soundcards can be quite expensive, and that only for the card
>itself, I would suspect, that that good computer/soundcard and good
>speaker combo can be as good as a good HiFi System?
>So I really don't know much about these things.

For word processing, the computer easily wins. For music reproduction, the
good HiFi will easily win.
------------
Alex
Anonymous
May 31, 2005 12:08:45 AM

Archived from groups: rec.audio.tech (More info?)

"calmar" <calmar@calmar.ws> wrote in message
news:slrnd9k37v.4ve.calmar@news.calmar.ws...
> Hi,
>
> I'm wondering, how a good computer with a good graphic card + good
> speakers can compare to a good HiFi System?

The graphic card will have no effect on the sound unless it is interfering
with the soundcard.

> Since good soundcards can be quite expensive, and that only for the card
> itself, I would suspect, that that good computer/soundcard and good
> speaker combo can be as good as a good HiFi System?

Yep, but the only part of a HiFi system that is different is the source.
Many soundcards exceed CD quality, but you still need HiFi amplification and
Speakers.

MrT.
Anonymous
May 31, 2005 1:14:58 AM

Archived from groups: rec.audio.tech (More info?)

On Mon, 30 May 2005 16:08:09 -0400, Alex Rodriguez <adr5@columbia.edu>
wrote:

>In article <slrnd9k37v.4ve.calmar@news.calmar.ws>, calmar@calmar.ws says...
>
>>Hi,
>>I'm wondering, how a good computer with a good graphic card + good
>>speakers can compare to a good HiFi System?
>>Since good soundcards can be quite expensive, and that only for the card
>>itself, I would suspect, that that good computer/soundcard and good
>>speaker combo can be as good as a good HiFi System?
>>So I really don't know much about these things.
>
>For word processing, the computer easily wins. For music reproduction, the
>good HiFi will easily win.

And your evidence for this is, what, exactly?
--

Stewart Pinkerton | Music is Art - Audio is Engineering
Anonymous
May 31, 2005 1:43:26 AM

Archived from groups: rec.audio.tech (More info?)

"calmar" <calmar@calmar.ws> wrote in message
news:slrnd9k81l.ei1.calmar@news.calmar.ws...

> Maybe it's possible to say some general things about these ways to play
> musik quality related?

Well, yes. With a computer-based system, you can play the audio files
directly, without first having to convert them to a hi-fi-friendly format
(eg CD), thus omitting the accompany audio degradation. Whether the
difference is detectable is debatable, of course.

Also, the computer-based system can use software processing. So you can,
for example, compensate for speaker driver impedance variations, without
having to build it into the speaker crossover or install a hardware EQ or
DSP system.

Tim
Anonymous
May 31, 2005 6:29:08 AM

Archived from groups: rec.audio.tech (More info?)

Joe Kesselman schreef:
> Geoff Wood wrote:
> > Also a computer doesn't generally look so great in the lounge, and doesn't
> > have a remote control.
>
> Depends on the model/accessories/software. Some are marketed as
> multimedia machines, and you can get remotes as peripherals, and the
> laptop I have dedicated to my stereo system is set up for remote control
> via the network.
>
> But that's offtopic for the question as asked. The real answer is: Given
> a good soundcard, and given non-compressed data (or losslessly
> compressed data), a PC can certainly be a "hi-fi" recording/playback system.

IMO, a computer using something like a Lynx studio technology soundcard
will compete with even the most expensive CD player and preamp. I run
my Lynx 2 direct to the poweramps and have never looked back. I sold my
Audio Research pre-amp. I used to be very reluctant to believe that
lossless compression would really work although rationally you know it
has to. I can't tell the difference even being blinded to comparisons.
I think the marriage of computer and hi-fi are here to stay; and that's
a good thing.

Wessel
Anonymous
May 31, 2005 6:10:58 PM

Archived from groups: rec.audio.tech (More info?)

In article <8i0n91pgla3bg5i5kc0khls4t42p5453nh@4ax.com>, patent3@dircon.co.uk
says...
>
>
>On Mon, 30 May 2005 16:08:09 -0400, Alex Rodriguez <adr5@columbia.edu>
>wrote:
>
>>In article <slrnd9k37v.4ve.calmar@news.calmar.ws>, calmar@calmar.ws says...
>>
>>>Hi,
>>>I'm wondering, how a good computer with a good graphic card + good
>>>speakers can compare to a good HiFi System?
>>>Since good soundcards can be quite expensive, and that only for the card
>>>itself, I would suspect, that that good computer/soundcard and good
>>>speaker combo can be as good as a good HiFi System?
>>>So I really don't know much about these things.
>>
>>For word processing, the computer easily wins. For music reproduction, the
>>good HiFi will easily win.
>
>And your evidence for this is, what, exactly?

No keyboard on the HiFI.
------------
Alex
Anonymous
May 31, 2005 9:10:31 PM

Archived from groups: rec.audio.tech (More info?)

Alex Rodriguez wrote:
> In article <8i0n91pgla3bg5i5kc0khls4t42p5453nh@4ax.com>,
> patent3@dircon.co.uk says...
>>
>>
>> On Mon, 30 May 2005 16:08:09 -0400, Alex Rodriguez
>> <adr5@columbia.edu> wrote:
>>
>>> In article <slrnd9k37v.4ve.calmar@news.calmar.ws>,
calmar@calmar.ws
>>> says...
>>>
>>>> Hi,
>>>> I'm wondering, how a good computer with a good graphic
card + good
>>>> speakers can compare to a good HiFi System?
>>>> Since good soundcards can be quite expensive, and that
only for
>>>> the card itself, I would suspect, that that good
>>>> computer/soundcard and good speaker combo can be as
good as a good
>>>> HiFi System?
>>>> So I really don't know much about these things.
>>>
>>> For word processing, the computer easily wins. For
music
>>> reproduction, the good HiFi will easily win.
>>
>> And your evidence for this is, what, exactly?
>
> No keyboard on the HiFI.

How does the keyboard detract from music reproduction on the
computer?
Anonymous
June 1, 2005 2:59:23 PM

Archived from groups: rec.audio.tech (More info?)

"Wessel Dirksen" <wdirksen@gmail.com> wrote in message
news:1117531748.282381.35020@z14g2000cwz.googlegroups.com...

> I used to be very reluctant to believe that
> lossless compression would really work although rationally you know it
> has to.

Any digital storage of an analog signal compresses it.

That is, for any method of storing an analog signal in x bits, it is
possible to devise a digital storage mechanism using >x bits which can be
used to reproduce a more accurate rendition of the original analog signal.

Tim
Anonymous
June 1, 2005 2:59:24 PM

Archived from groups: rec.audio.tech (More info?)

Tim Martin wrote:

> "Wessel Dirksen" <wdirksen@gmail.com> wrote in message
>
news:1117531748.282381.35020@z14g2000cwz.googlegroups.com...

>> I used to be very reluctant to believe that
>> lossless compression would really work although
rationally you know
>> it has to.

> Any digital storage of an analog signal compresses it.

However to be fair we must say that the best commonly-used
(e.g. CD audio) digital storage almost always compresses the
signal less than analog storage.

> That is, for any method of storing an analog signal in x
bits, it is
> possible to devise a digital storage mechanism using >x
bits which
> can be used to reproduce a more accurate rendition of the
original
> analog signal.

In general the better digital storage formats (e.g. CD
audio) have far greater resolution than the analog signals
they store.
Anonymous
June 1, 2005 8:28:28 PM

Archived from groups: rec.audio.tech (More info?)

On Wed, 01 Jun 2005 10:59:23 GMT, "Tim Martin"
<tim2718281@ntlworld.com> wrote:

>"Wessel Dirksen" <wdirksen@gmail.com> wrote in message
>news:1117531748.282381.35020@z14g2000cwz.googlegroups.com...
>
>> I used to be very reluctant to believe that
>> lossless compression would really work although rationally you know it
>> has to.
>
>Any digital storage of an analog signal compresses it.

No, it doesn't. This is utter nonsense, but a persistent urban myth.

>That is, for any method of storing an analog signal in x bits, it is
>possible to devise a digital storage mechanism using >x bits which can be
>used to reproduce a more accurate rendition of the original analog signal.

That's not even theoretically true. Provided that the dynamic range of
the analogue signal, i.e. the range from peak level to noise floor,
can be accommodated within the quoted number of bits, then adding bits
will provide *zero* extra accuracy.

For example, no known music *master* tape hasa dynamic range exceeding
85dB, due to microphone self-noise among other factors, which may be
represented by a fraction more than 14 bits. Hence, 16-bit sampling is
more than adequate for any musical *replay* medium. You'll ideally
have a little more at the recording end, to cater for EQ and
accidental microphone overloads on some tracks, so the ubiquitous
24/96 is useful here, but 16 bits will be more than adequate for the
final mixdown master, and hence for the replay medium.
--

Stewart Pinkerton | Music is Art - Audio is Engineering
Anonymous
June 1, 2005 9:13:41 PM

Archived from groups: rec.audio.tech (More info?)

TIm Martin intoned:
>Any digital storage of an analog signal compresses it.

You want to bet on that? If you do, consider who's going to be
wagering against you:

Blesser, B.A., "Digitization of Audio: A Comprehensive
Examination of Theory, Implementation, and Current
Practice," JAES, vol. 26, no. 10, October, 1978.
"Elementary and Basic Aspects of Digital Audio," AES
Digital Audio Collected Papers, Rye, 1983.
Nyquist, H., "Certain Factors Affecting Telegraph Speed,"
Bell Sys. Tech. Journal, vol. 3, no. 2, April, 1924.
"Certain Topics in Telegraph Transmission Theory," Trans.
AIEE, vol. 47, no. 2, April, 1928
Shannon, C.E., "A Mathematical Theory of Communication,"
Bell Sys. Tech. Journal, vol. 27, October, 1948.
Vanderkooy, J., and S.P. Lipshitz, "Dither in Digital Audio,"
JAES, vol. 35, no. 12, December, 1987.
"Resolution Below the Least Significant Bit in Digital Audio
Systems with Dither," JAES, vol. 32, no. 3, March, 1984,
Erratum, JAES, vol. 32, no. 11, November, 1984.

There are probably 12-15 other articles that you'll want to study
before you lose your hard earned money betting on an ill-advised
position.

>That is, for any method of storing an analog signal in x bits,
>it is possible to devise a digital storage mechanism using >x bits
>which can be used to reproduce a more accurate rendition of the
>original analog signal.

Your assertion directly infers that you can measure any signal
with arbitrary accuracy. To do that requires a system that has
infinite bandwidth and infinite dynamic range. The practical
requirements for that is the necessity of infinite time and
energy.

Beyond what may seem to be a philosphical discussion (it isn't:
it's a direct and inevitable consequence of the your basic
assertion and is proven rigorously in work cited above by Nyquist
and Shannon), the simplem fact is that ANY system of a finite
bandwidth and limited dynamic range can be EXACTLY represented
by a quantized system of finite accuracy.

Nyquist and Shannon show that for a bandwidth of Fb, a sample
rate in excess of 2*Fb is necessary AND sufficient to sample
the signal in the time domain with NO loss in information. In
a similar fashion, they rigorously showed that to fully capture
with NO loss, a signal with a dynamic range of x dB, a sample
size of x/6.02 bits is required (since in binary representation,
the resolution is 6.02 dB/bit.

Assume that a bandwidth of 20 kHz, a sample rate in excess of
2*20 kHz is sufficient to capture the information in the time
with NO loss. Assume a dynamic range (noise floor to maximum
possible level) of 80 dB (VERY generous for LPs), 80/6.02 or
13.3 bits is needed to sufficiently sample in the amplitude
domain with NO loss of accuracy. Increasing the sample rate
or the word size, contrary to your assertion, will NOT produce
any more accuracy.

Thus, a sample rate of 44.1 kHz and a word size of 16 bits can
be shown to be more than sufficient to encode LPs with no loss
or compression at all.

Them's the facts. Do with them what you will.

But I would recommend you not bet against them and I would
also recommend that you not continue to spread misinformation
of the sort:

"Any digital storage of an analog signal compresses it."
June 1, 2005 10:27:15 PM

Archived from groups: rec.audio.tech (More info?)

>>Any digital storage of an analog signal compresses it.
>
> No, it doesn't. This is utter nonsense, but a persistent urban myth.

No storage of any analog signal is perfect, whether you digitize it or not.
There are errors with digital storage but there are also errors with analog
storage.

With digital, once you've encoded the signal, you can store and retrieve it
with no further change. Not with analog.

Getting back to the question of whether there is such a thing as lossless
compression of digital signals: Yes, certainly. The simplest is run-length
encoding. Whenever a value recurs (e.g., a long series of zeroes for a
period of silence), instead of repeating the value over and over, you
precede it with a code that means "repeat this value such-and-such number of
times."
Anonymous
June 1, 2005 11:27:04 PM

Archived from groups: rec.audio.tech (More info?)

"Tim Martin" wrote ...
> Any digital storage of an analog signal compresses it.

You'd better explain that if you don't want people to think you
are completely daft.

> That is, for any method of storing an analog signal in x bits, it is
> possible to devise a digital storage mechanism using >x bits which can be
> used to reproduce a more accurate rendition of the original analog signal.

Do you have some magic method of creating additional data where
there was none before? Don't even answer this message, rush down
and patent it and become an instant millionaire.
Anonymous
June 2, 2005 12:59:25 AM

Archived from groups: rec.audio.tech (More info?)

Tim Martin wrote:
> That is, for any method of storing an analog signal in x bits, it is
> possible to devise a digital storage mechanism using >x bits which can be
> used to reproduce a more accurate rendition of the original analog signal.

Well, yes, analog is _theoretically_ infinite precision. And 1 is
theoretically different from
..999999999999999999999999999999999999999999999999999999999999999999999999999
.... but for most practical purposes, "good enough" really is Good
Enough. Human hearing is not infinitely accurate. Nor is any real-world
recording medium.

Digital beats the accuracy of most analog media quite handily, given a
suprisingly small investment. The limiting factor, actually, tends to be
the analog hardware used to get the signal into and out of digital form.
Anonymous
June 2, 2005 1:00:57 AM

Archived from groups: rec.audio.tech (More info?)

Alex Rodriguez wrote:
> For word processing, the computer easily wins. For music reproduction, the
> good HiFi will easily win.

Your CD player is a computer. Most of the music you're hearing these
days passed through computers before it reached you. I'm sorry, but you
really don't know what you're talking about.
Anonymous
June 2, 2005 1:00:58 AM

Archived from groups: rec.audio.tech (More info?)

"Joe Kesselman" wrote ..
> Alex Rodriguez wrote:
> > For word processing, the computer easily wins. For music reproduction,
the
> > good HiFi will easily win.
>
> Your CD player is a computer. Most of the music you're hearing these
> days passed through computers before it reached you. I'm sorry, but you
> really don't know what you're talking about.

Certainly EVERYTHING you hear over the air and EVERYTHING you can
buy on CD passed through several "computers" of various kinds. You'd have
to go to a vintage record store to find pure-analog recordings these days.
Anonymous
June 2, 2005 1:01:48 AM

Archived from groups: rec.audio.tech (More info?)

OK, it's clear that some of the folks on this topic are just here to
troll. Since they're incurable, I'm gone.
Anonymous
June 2, 2005 1:04:38 AM

Archived from groups: rec.audio.tech (More info?)

On Wed, 01 Jun 2005 10:59:23 GMT, "Tim Martin"
<tim2718281@ntlworld.com> wrote:

>Any digital storage of an analog signal compresses it.
>
>That is, for any method of storing an analog signal in x bits, it is
>possible to devise a digital storage mechanism using >x bits which can be
>used to reproduce a more accurate rendition of the original analog signal.

You don't understand sampling, do you? :-)
Anonymous
June 2, 2005 12:01:03 PM

Archived from groups: rec.audio.tech (More info?)

"Tim Martin" <tim2718281@ntlworld.com> wrote in message
news:fygne.4449$ci4.544@newsfe6-win.ntli.net...
>
> "Wessel Dirksen" <wdirksen@gmail.com> wrote in message
> news:1117531748.282381.35020@z14g2000cwz.googlegroups.com...
>
>> I used to be very reluctant to believe that
>> lossless compression would really work although rationally you know it
>> has to.
>
> Any digital storage of an analog signal compresses it.
>
> That is, for any method of storing an analog signal in x bits, it is
> possible to devise a digital storage mechanism using >x bits which can be
> used to reproduce a more accurate rendition of the original analog signal.

What if the original x bits has more resolution than the original media ?

geoff
June 2, 2005 12:01:04 PM

Archived from groups: rec.audio.tech (More info?)

>> That is, for any method of storing an analog signal in x bits, it is
>> possible to devise a digital storage mechanism using >x bits which can be
>> used to reproduce a more accurate rendition of the original analog
>> signal.
>
> What if the original x bits has more resolution than the original media ?

If it has sufficiently more, then the digital copy will be at least as
accurate as any analog copy.
Anonymous
June 2, 2005 5:43:00 PM

Archived from groups: rec.audio.tech (More info?)

In article <l5ednQWyVKVaTwHfRVn-3g@comcast.com>, arnyk@hotpop.com says...
>
>
>Alex Rodriguez wrote:
>> In article <8i0n91pgla3bg5i5kc0khls4t42p5453nh@4ax.com>,
>> patent3@dircon.co.uk says...
>>>
>>>
>>> On Mon, 30 May 2005 16:08:09 -0400, Alex Rodriguez
>>> <adr5@columbia.edu> wrote:
>>>
>>>> In article <slrnd9k37v.4ve.calmar@news.calmar.ws>,
>calmar@calmar.ws
>>>> says...
>>>>
>>>>> Hi,
>>>>> I'm wondering, how a good computer with a good graphic
>card + good
>>>>> speakers can compare to a good HiFi System?
>>>>> Since good soundcards can be quite expensive, and that
>only for
>>>>> the card itself, I would suspect, that that good
>>>>> computer/soundcard and good speaker combo can be as
>good as a good
>>>>> HiFi System?
>>>>> So I really don't know much about these things.
>>>>
>>>> For word processing, the computer easily wins. For
>music
>>>> reproduction, the good HiFi will easily win.
>>>
>>> And your evidence for this is, what, exactly?
>>
>> No keyboard on the HiFI.
>
>How does the keyboard detract from music reproduction on the
>computer?

No keyboard on the HiFi makes it hard to use it for word processing. :) 
----------------
Alex
Anonymous
June 2, 2005 6:58:08 PM

Archived from groups: rec.audio.tech (More info?)

Joe Kesselman wrote:
> Tim Martin wrote:
> > That is, for any method of storing an analog signal in x bits, it
> > is possible to devise a digital storage mechanism using >x bits
> > which can be used to reproduce a more accurate rendition of the
> > original analog signal.
>
> Well, yes, analog is _theoretically_ infinite precision.

No, it is not, not even theoretically.

Because for there to be infinite resolution for any arbitrary
signal, even in theory, there must be infinite signal-to-noise,
because the presence of noise limits the resolution of the signal
to a level of ambiguity defined by the level of the noise. And since
no noise requires that the system operate at a teemperature of
precisely 0 degrees K, the introduction of ANY signal into such
a system will be the equivalent of raising itsd temperature and in
and of itself introduces noise. SO that shifts the requirement to
having a finite noise floor. And a finite noise floor, even one
which is vanishngly small, requires that to achieve the infinite
dynamic range that is intrinsic of infinite resolution requires
signals of infinite amplitude, which means infinite energy.

And even if we ignore all that, we're bitten by the fact of simple
quantum uncertainty, which prevents perfect knowledge of a system.

And further, to have infinite resolution in the time domain requires
the system to have infinite bandwidth. Since bandwidth and time are
related by the fundamental time-frequency uncertainty relationship,
the only way to have infinite resolution in the time domain, i.e.,
the ability to distinguish to event separated by infinitesimal time,
the system must exist for infinite time.

And the assertion that analog has infinite time resolution means
that ANY change in level in a an infintiesimal period of time
intrinisically requires infinite energy.

So, no even THEORETICALLY, analog does not, indeed, CANNOT have
infinite resolution. To claim so is absurd.

> ... but for most practical purposes, "good enough" really is Good
> Enough. Human hearing is not infinitely accurate. Nor is any real-world
> recording medium.

Or even a theoretical one.

> Digital beats the accuracy of most analog media quite handily, given a
> suprisingly small investment. The limiting factor, actually, tends to be
> the analog hardware used to get the signal into and out of digital form.

Indeed, this is often the case.

And, as Shannon quite rigorously demonstrated over half a century ago,
any system sampling at more than twice the bandwidth of the signal
and simply having sufficient bits (dynamic range in dB/6.02 db/bit)
WILL encode that signal with perfect accuracy. Increasing the sample
rate or the bit depth WILL not result in ANY more accuracy, just a
waste
of data bandwidth.
Anonymous
June 3, 2005 6:07:30 AM

Archived from groups: rec.audio.tech (More info?)

"Stewart Pinkerton" <patent3@dircon.co.uk> wrote in message
news:s7or915iebk5j0754tiiivkr2njjm2f94c@4ax.com...

> For example, no known music *master* tape hasa dynamic range exceeding
> 85dB, due to microphone self-noise among other factors, which may be
> represented by a fraction more than 14 bits. Hence, 16-bit sampling is
> more than adequate for any musical *replay* medium.

What have tapes and microphones got to do with it? I was talking about
analog signals, not recorded approximations of analog signals.

Tim
Anonymous
June 3, 2005 6:07:31 AM

Archived from groups: rec.audio.tech (More info?)

"Tim Martin" wrote ...
> "Stewart Pinkerton" wrote ...
>> For example, no known music *master* tape has a dynamic
>> range exceeding 85dB, due to microphone self-noise among
>> other factors, which may be represented by a fraction more
>> than 14 bits. Hence, 16-bit sampling is more than adequate
>> for any musical *replay* medium.
>
> What have tapes and microphones got to do with it? I was
> talking about analog signals, not recorded approximations
> of analog signals.

How did your "analog signals" originate? How did they then
end up as ones and zeroes on a tape or disc?

Just to confirm: Most of us are reading this newsgroup on
"Earth" in the "Solar System" of the "Milky Way" galaxy.
If you are posting from a different galaxy (or universe) we
may have to attempt some understanding of each other's laws
of physics.
Anonymous
June 3, 2005 6:19:12 AM

Archived from groups: rec.audio.tech (More info?)

<dpierce@cartchunk.org> wrote in message
news:1117671221.564785.245640@g43g2000cwa.googlegroups.com...

> Beyond what may seem to be a philosphical discussion (it isn't:
> it's a direct and inevitable consequence of the your basic
> assertion and is proven rigorously in work cited above by Nyquist
> and Shannon), the simplem fact is that ANY system of a finite
> bandwidth and limited dynamic range can be EXACTLY represented
> by a quantized system of finite accuracy.

An analog signal, such as a bird singing in the woods, has infinite
bandwidth.

That is, there is no upper frequency f, such that any combination of waves
of frequency less than f, can exactly represent an arbitrary analog signal,
regardless of the precision of the waves.

Nyquist's Theoerem is about representation of periodic signals; most sounds
are not periodic signals.

Of course in practice we can specify a combinations of waves that make close
approximations to the bird singing; and we can get as close as we like, up
to the limits of whatever equipment we use to detect the analog signal we
are approximating.

Tim
Anonymous
June 3, 2005 6:19:13 AM

Archived from groups: rec.audio.tech (More info?)

"Tim Martin" wrote ...
> An analog signal, such as a bird singing in the woods, has infinite
> bandwidth.

Baloney. Assuming you are talking about a REAL woods and
REAL birds.

> That is, there is no upper frequency f, such that any combination
> of waves of frequency less than f, can exactly represent an arbitrary
> analog signal, regardless of the precision of the waves.

Of course there is an upper frequency limit . If you are talking
about near-field (within milimeters of the REAL bird), you have
the limitation that the sounds are produced by organic structures
with mass that can move only so fast. And in the diffuse field,
you can add to that the HF attenuation of the atmosphere in the
REAL woods.

> Nyquist's Theoerem is about representation of periodic signals;
> most sounds are not periodic signals.
>
> Of course in practice we can specify a combinations of waves
> that make close approximations to the bird singing; and we can
> get as close as we like, up to the limits of whatever equipment
> we use to detect the analog signal we are approximating.

And the problem with that is....
Anonymous
June 3, 2005 6:38:17 AM

Archived from groups: rec.audio.tech (More info?)

"Richard Crowley" <rcrowley7@xprt.net> wrote in message
news:119vfc5o62hbt00@corp.supernews.com...

> How did your "analog signals" originate?

A bird singing in the woods. This generates an analog signal, detectable by
ears.

> How did they then end up as ones and zeroes on a tape or disc?

It's possible to store a digital approximation of this analog signal by a
number of methods; I don't see that it actually matters what method is
used, but I suppose the most direct method is to have some flexible device
that vibrates with the sound of the bird singing, and periodically measure
the physical position of the flexible device.

The more frequently we measure the position, and the more precisely we
measure the position, the more accurate is our digital representation of the
analog signal.

Tim
Anonymous
June 3, 2005 6:42:25 AM

Archived from groups: rec.audio.tech (More info?)

"Joe Kesselman" <keshlam-nospam@comcast.net> wrote in message
news:brCdna2kvYJ-xAPfRVn-sA@comcast.com...
>
> Digital beats the accuracy of most analog media quite handily, given a
> suprisingly small investment. The limiting factor, actually, tends to be
> the analog hardware used to get the signal into and out of digital form.

Yes. However, since digital representations of analog signals are
compressed, there is little point agonizing over "lossy" versus "lossless"
compresssion. What matters is the quality delivered.

Tim
Anonymous
June 3, 2005 6:42:26 AM

Archived from groups: rec.audio.tech (More info?)

"Tim Martin" <tim2718281@ntlworld.com> wrote in message
news:lsPne.21$BQ3.15@newsfe3-win.ntli.net...
>
> "Joe Kesselman" <keshlam-nospam@comcast.net> wrote in message
> news:brCdna2kvYJ-xAPfRVn-sA@comcast.com...
>>
>> Digital beats the accuracy of most analog media quite handily, given
>> a
>> suprisingly small investment. The limiting factor, actually, tends to
>> be
>> the analog hardware used to get the signal into and out of digital
>> form.
>
> Yes. However, since digital representations of analog signals are
> compressed,

Unless you show some support for this fantastic statement,
there doesn't appear to be any point in continuing this dialog.
Anonymous
June 3, 2005 7:36:53 AM

Archived from groups: rec.audio.tech (More info?)

On Thu, 2 Jun 2005 19:16:36 -0700, "Richard Crowley"
<rcrowley7@xprt.net> wrote:

>"Tim Martin" wrote ...

>> What have tapes and microphones got to do with it? I was
>> talking about analog signals, not recorded approximations
>> of analog signals.

What exactly are "analog signals"? Going back a few decades, what
exactly were (and still are) analog computers, and what were they used
for?

>How did your "analog signals" originate? How did they then

Furthermore, what is the meaning of the word "analog"?

>end up as ones and zeroes on a tape or disc?
>
>Just to confirm: Most of us are reading this newsgroup on
>"Earth" in the "Solar System" of the "Milky Way" galaxy.
>If you are posting from a different galaxy (or universe) we
>may have to attempt some understanding of each other's laws
>of physics.

As well as other analogous laws...
-----
http://mindspring.com/~benbradley
Anonymous
June 3, 2005 7:49:16 AM

Archived from groups: rec.audio.tech (More info?)

On Fri, 03 Jun 2005 02:42:25 GMT, "Tim Martin"
<tim2718281@ntlworld.com> wrote:

>
>"Joe Kesselman" <keshlam-nospam@comcast.net> wrote in message
>news:brCdna2kvYJ-xAPfRVn-sA@comcast.com...
>>
>> Digital beats the accuracy of most analog media quite handily, given a
>> suprisingly small investment. The limiting factor, actually, tends to be
>> the analog hardware used to get the signal into and out of digital form.
>
>Yes. However, since digital representations of analog signals are
>compressed, there is little point agonizing over "lossy" versus "lossless"
>compresssion.

You stated something very similar earlier in the thread (6/01/05,
6:59AM, in response to Wessel Dirksen) It appears you may be confusing
dynamic (volume or signal amplitude) compression with data compression
(as defined in computer science), but it's really hard to tell.
Please be very specific on what you mean by "digital
representations of analog signals are compressed."

>What matters is the quality delivered.

I agree with that, but I don't see how that follows from what you
wrote earlier.

>Tim
>

-----
http://mindspring.com/~benbradley
Anonymous
June 3, 2005 10:50:12 AM

Archived from groups: rec.audio.tech (More info?)

On Fri, 03 Jun 2005 02:07:30 GMT, "Tim Martin"
<tim2718281@ntlworld.com> wrote:

>
>"Stewart Pinkerton" <patent3@dircon.co.uk> wrote in message
>news:s7or915iebk5j0754tiiivkr2njjm2f94c@4ax.com...
>
>> For example, no known music *master* tape has a dynamic range exceeding
>> 85dB, due to microphone self-noise among other factors, which may be
>> represented by a fraction more than 14 bits. Hence, 16-bit sampling is
>> more than adequate for any musical *replay* medium.
>
>What have tapes and microphones got to do with it? I was talking about
>analog signals, not recorded approximations of analog signals.

Stop being disingenuous, you were just plain *wrong*, live with it.
--

Stewart Pinkerton | Music is Art - Audio is Engineering
Anonymous
June 3, 2005 10:52:02 AM

Archived from groups: rec.audio.tech (More info?)

On Fri, 03 Jun 2005 02:42:25 GMT, "Tim Martin"
<tim2718281@ntlworld.com> wrote:

>"Joe Kesselman" <keshlam-nospam@comcast.net> wrote in message
>news:brCdna2kvYJ-xAPfRVn-sA@comcast.com...
>>
>> Digital beats the accuracy of most analog media quite handily, given a
>> suprisingly small investment. The limiting factor, actually, tends to be
>> the analog hardware used to get the signal into and out of digital form.
>
>Yes. However, since digital representations of analog signals are
>compressed, there is little point agonizing over "lossy" versus "lossless"
>compresssion.

No, they're not. Please read up on digital audio before you spout this
nonsense.

> What matters is the quality delivered.

And digital far exceeds the quality of any available analogue source
signal.
--

Stewart Pinkerton | Music is Art - Audio is Engineering
Anonymous
June 3, 2005 11:05:22 AM

Archived from groups: rec.audio.tech (More info?)

Tim Martin wrote:
> "Richard Crowley" <rcrowley7@xprt.net> wrote in message
> news:119vfc5o62hbt00@corp.supernews.com...
>
>> How did your "analog signals" originate?
>
> A bird singing in the woods. This generates an analog
signal,
> detectable by ears.

However, the dynamic range in the woods is not all that
good, because the background noise level in the woods is
pretty high compared to bird songs, especially with the
typical distances involved. Nature can be pretty noisy.
Leaves rustle, the wind has turbulence problems, waves lap
or crash, insects buzz...

>> How did they then end up as ones and zeroes on a tape or
disc?

> It's possible to store a digital approximation of this
analog signal
> by a number of methods; I don't see that it actually
matters what
> method is used, but I suppose the most direct method is to
have some
> flexible device that vibrates with the sound of the bird
singing, and
> periodically measure the physical position of the flexible
device.

IOW a microphone.

> The more frequently we measure the position, and the more
precisely we
> measure the position, the more accurate is our digital
representation
> of the analog signal.

Wrong. While taking more measurements in the time domain
increases the highest frequency that can be reliably
discerned, it does nothing for resolution or accuracy of the
measurements. If you want accuracy, you have to improve the
quality of each measurement.
Anonymous
June 3, 2005 11:11:16 AM

Archived from groups: rec.audio.tech (More info?)

Tim Martin wrote:
> <dpierce@cartchunk.org> wrote in message
>
news:1117671221.564785.245640@g43g2000cwa.googlegroups.com...
>
>> Beyond what may seem to be a philosphical discussion (it
isn't:
>> it's a direct and inevitable consequence of the your
basic
>> assertion and is proven rigorously in work cited above by
Nyquist
>> and Shannon), the simplem fact is that ANY system of a
finite
>> bandwidth and limited dynamic range can be EXACTLY
represented
>> by a quantized system of finite accuracy.
>
> An analog signal, such as a bird singing in the woods, has
infinite
> bandwidth.

Not really. Creating sounds at an infinitely high frequency
requires infinite amounts of energy.

> That is, there is no upper frequency f, such that any
combination of
> waves of frequency less than f, can exactly represent an
arbitrary
> analog signal, regardless of the precision of the waves.

In reality the energy in bird calls and other natural sounds
at high frequencies is limited and naturally rolling off,
and at some surprisingly low frequency, it drops below the
noise floor.

> Nyquist's Theoerem is about representation of periodic
signals; most
> sounds are not periodic signals.

All real world sounds can be sucessfully analyzed as a
collection of enveloped periodic signals. Fourier wasn't
wrong.

> Of course in practice we can specify a combinations of
waves that
> make close approximations to the bird singing; and we can
get as
> close as we like, up to the limits of whatever equipment
we use to
> detect the analog signal we are approximating.

Same basic problems and results irregardless of whether the
test equipment is analog or digital. Digital test equipment
tends to have better price performance. The lowest noise
floors in audio test equipment generally are obtained with
equipment that is mostly digital. For example, Wein bridges
have built-in dynamic range problems when you actually try
to implement one practically and economically.
Anonymous
June 3, 2005 11:32:01 AM

Archived from groups: rec.audio.tech (More info?)

On Fri, 03 Jun 2005 02:19:12 GMT, "Tim Martin"
<tim2718281@ntlworld.com> wrote:

>
><dpierce@cartchunk.org> wrote in message
>news:1117671221.564785.245640@g43g2000cwa.googlegroups.com...
>
>> Beyond what may seem to be a philosphical discussion (it isn't:
>> it's a direct and inevitable consequence of the your basic
>> assertion and is proven rigorously in work cited above by Nyquist
>> and Shannon), the simplem fact is that ANY system of a finite
>> bandwidth and limited dynamic range can be EXACTLY represented
>> by a quantized system of finite accuracy.
>
>An analog signal, such as a bird singing in the woods, has infinite
>bandwidth.

Utter garbage! Everything generating noise in the woods has a very
well defined bandwidth,dependent on the mass/compliance resonaces of
its suspension systems. This includes the larynxes of birds. Also, the
atmosphere has a well-defined sound absorption coefficient which
increases with frequency, such that even a metre away from that bird,
you won't detect much above 100kHz. That's why bats don't have to
worry about reflections from more than a few yards away, the signal
simply doesn't get back to them.

More importantly, since you seem to understand almost nothing which
you are spouting, these are *not* analogue sugnals, they are simply
sounds. Once you have *converted* that sound with say a microphone,
you then have a signal which is an analogue of the original sound. The
live microphone feed is the analogue signal, *not* the original sound.

>That is, there is no upper frequency f, such that any combination of waves
>of frequency less than f, can exactly represent an arbitrary analog signal,
>regardless of the precision of the waves.

However, since there definitely *is* an upper frequency limit to
birdsong, that's not actually a problem.

>Nyquist's Theoerem is about representation of periodic signals; most sounds
>are not periodic signals.

Actually, it's not, except in so far as it does have a bandwidth limit
of less than half the sampling frequency.

>Of course in practice we can specify a combinations of waves that make close
>approximations to the bird singing; and we can get as close as we like, up
>to the limits of whatever equipment we use to detect the analog signal we
>are approximating.

The analogue signal from the microphone *is* the approximation of the
original sound. At least learn the *basics*, then you wouldn't make
such nonsensical statements.
--

Stewart Pinkerton | Music is Art - Audio is Engineering
Anonymous
June 3, 2005 11:49:06 AM

Archived from groups: rec.audio.tech (More info?)

> Nyquist's Theoerem is about representation of periodic signals; most
> sounds
> are not periodic signals.

Any arbitrary sound can be decomposed into a sum of periodic signals.
Therefore, Nyquist's theorem applies to all sounds.
Anonymous
June 3, 2005 12:38:18 PM

Archived from groups: rec.audio.tech (More info?)

"Karl Uppiano" <karl.uppiano@verizon.net> wrote in message
news:SXTne.16106$qJ3.7554@trnddc05...
> > Nyquist's Theoerem is about representation of periodic signals; most
> > sounds
> > are not periodic signals.
>
> Any arbitrary sound can be decomposed into a sum of periodic signals.

OK; let's suppose the sound consists of silence, followed by one second of
1kHz sine wave, followed by silence.

What sum of periodic signals can this be decomposed into?

Tim
Anonymous
June 3, 2005 2:43:44 PM

Archived from groups: rec.audio.tech (More info?)

Tim Martin wrote:
> "Karl Uppiano" <karl.uppiano@verizon.net> wrote in message
> news:SXTne.16106$qJ3.7554@trnddc05...
> > > Nyquist's Theoerem is about representation of periodic signals; most
> > > sounds
> > > are not periodic signals.
> >
> > Any arbitrary sound can be decomposed into a sum of periodic signals.
>
> OK; let's suppose the sound consists of silence, followed by one second of
> 1kHz sine wave, followed by silence.
>
> What sum of periodic signals can this be decomposed into?

It's exactly the same as a 1 kHz sine wave 100% modulated by a 0.5
Hz square wave, and such decomposes into a series of sine components
spaced 1 Hz apart spaced symmetrically about the 1 kHz component
offset from it by 0.5 Hz, (iow 1000.5, 1001.5, 1002.5, 999.5, 998.5,
997.5, ...) with amplitudes decreasing as we move away from 1 kHz by
a simple 1/n, n = 1, 3, 5, ... and so forth, all components in phase.

AND, if you insist on truning on and off the sine wave INSTANTANEOUSLY,
these sine components extend to +-infinite frequency.

Such a signal, as I am sure you will agree, could never be PRODUCED
perfectly in ANY system existing for finite time or limited to finite
energy.
Anonymous
June 3, 2005 2:47:13 PM

Archived from groups: rec.audio.tech (More info?)

"Stewart Pinkerton" <patent3@dircon.co.uk> wrote in message
news:mhvv9118jips49mc63o6c90c1lr0qt9ng0@4ax.com...

Tim

> >Nyquist's Theoerem is about representation of periodic signals; most
sounds
> >are not periodic signals.

Stewart

> Actually, it's not, except in so far as it does have a bandwidth limit
> of less than half the sampling frequency.

Nyquist's Theorem tells us we can exactly represent the information in a
waveform by sampling it at a rate at least twice as high as the highest
frequency in the waveform

I think there's an implication here that by "highest frequency", we are
talking about the highest frequency in a Fourier transform of the original
signal. And the Fourier transform applies only to periodic signals.

Take a waveform consisting of, say a 1000Hz sine wave that is repeatedly
switched on and off at random times. This is not a periodic waveform, and
cannot be represented exactly by a Fourier transform. It has infinite
bandwidth. (Conceptually at least. As you've previously remarked, there
are physical constraints imposed by the transmission medium.)

So what happens when we try to represent that wavefom by a digital
representation (and I'm thinking here of a general-purpose digital
representation.) To keep things simple, let's suppose the amplitude of the
sine wave is small, so gives rise to only two different digital values, 0
and 1.

If we are sampling 48000 times a second, and if the sine wave is long enough
when on, our digital signal will, after some start-up sequence, consist of a
repeating pattern of 24 ones followed by 24 zeroes. Once we're in this part
of the signal, we can reproduce the original sine wave exactly (within the
resolution limits, which are not the issue here.)

But when does our reproduction start?

Our digital representation will have an initial series of values
representing the silence. Again leaving aside start-up considerations, a
series of 48000 identical values will represent one second's initial
silence, and 48001 will represent 1.000021 seconds of silence.

All silent intervals between 1 and 1.000021 seconds will be represented by
one of these values. And as there are more than 2 different analog signals
starting with between 1 and 1.000021 seconds of silence, we are losing
information in the digital representation ... that is, we are compressing
it.

All this is straightforward maths.

I think where you went wrong is failing to distinguish between the audio
frequencies contained in the signal, and the timing information contained in
the signal. In hi-fi, this doesn't usually matter - correctly reproducing
the audio frequencies gives us more than enough timing precision - but in
information theory it does.

Tim
Anonymous
June 3, 2005 5:32:36 PM

Archived from groups: rec.audio.tech (More info?)

"Arny Krueger" <arnyk@hotpop.com> wrote in message
news:2KadnR34zaLvpD3fRVn-sw@comcast.com...

> However, the dynamic range in the woods is not all that
> good, because the background noise level in the woods is
> pretty high compared to bird songs, especially with the
> typical distances involved. Nature can be pretty noisy.

Careful - that's all part of the signal, not "noise". If we were trying to
reproduce the sound of a bird singing in the woods, we would want the
background sound, too.

> IOW a microphone.

Yes, it's pretty much what a capacitor microphone does fairly directly..
However, microphones generate electrical signals, which are affected by the
circuitry they are connected to - that is, the microphone introduces noise -
and I didn't want to confuse the issue with that, hence my suggesting we
measure the position of a moving element.

> > The more frequently we measure the position, and the more
> precisely we
> > measure the position, the more accurate is our digital
> representation
> > of the analog signal.
>
> Wrong. While taking more measurements in the time domain
> increases the highest frequency that can be reliably
> discerned, it does nothing for resolution or accuracy of the
> measurements. If you want accuracy, you have to improve the
> quality of each measurement.

Bear in mind that the context I set was an analog signal with infinite
bandwidth ... eg including sounds starting and stopping at arbitrary times.
So improving the timing resolution does improve the accuracy of the digital
representation.

If we take measurements 10,000 times a second, our resolution is 0.0001
seconds , our digital representation won't necessarily be able to
distinguish between sounds starting at 1.00001 seconds and sounds starting
at 1.00002 seconds; whereas if we take measurements 100,000 times a second,
it will be able to.

Tim
Anonymous
June 3, 2005 5:47:35 PM

Archived from groups: rec.audio.tech (More info?)

"Arny Krueger" <arnyk@hotpop.com> wrote in message
news:sdednURrFd9Ipz3fRVn-gA@comcast.com...

> Not really. Creating sounds at an infinitely high frequency
> requires infinite amounts of energy.

The scenario does not include any sounds of infinitely high frequency. We
can stick with just two tones: one silence, and the other a single tone of
1000Hz.

What I'm saying is that it's not possible to accurately represent a sound
consisting of alternate arbitrary-length sequences of 1000Hz sine waves and
silence with any set of sine waves. regardless of the upper frequency we
use. And that it's not possible to represent them by any digital signal
with fixed sampling frequency, no matter how high that sampling frequency
is.

To put it another way: for any fixed-sampling-frequency digital
representation you specify, I can define two different non-periodic analog
signals, using only silence and 1000 Hz sine waves, that will both map to
the same digital representation.

This is trivial. .

Tim.
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