HiFi vs. Computer

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
134 answers Last reply
More about hifi computer
  1. 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.
  2. 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. :-)
  3. 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
  4. 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).
  5. 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 *
    *******************************************
  6. 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
  7. 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.
  8. 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
  9. 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.
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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?
  15. 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
  16. 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.
  17. 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
  18. 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."
  19. 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."
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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? :-)
  26. 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
  27. 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.
  28. 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
  29. 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.
  30. 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
  31. 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.
  32. 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
  33. 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....
  34. 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
  35. 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
  36. 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.
  37. 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
  38. 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
  39. 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
  40. 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
  41. 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.
  42. 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.
  43. 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
  44. 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.
  45. 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
  46. 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.
  47. 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
  48. 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
  49. 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.
Ask a new question

Read More

Speakers Computers Sound Cards Audio