[EMAIL PROTECTED] wrote:
>
> At 11:01 AM 7/19/99 +0100, Barnesey wrote:
>
> >> Kade Hansson wrote an informative piece about audio formats, but:
> >>
> >>
> >> A 22kHz sine wave is on the fringe of human heaing. However, a CD will
> >> convert this to a square wave,
> >>
> > I think the input from the master is filtered to remove all
> >frequencies above some frequency slightly BELOW 22 kHz. And the CD would not
> >reproduce a 22 kHz sine wave as a square wave, because of the output
> >filtering, which would remove the harmonics, leaving a fairly smooth sine
> >wave.
>
> You are probably right. But I am a digital man, and a wave form is a series
> of flat steps lasting for 1/frequency. For me, if a signal is +32767 for
> 1/44.1 ms and then -32767 for 1/44.1 ms in the next sample, we have a
> square wave. I am glad CD players smooth this into a sine/sawtooth wave
> (assuming infinitesimal samples), but then we have the same problem for
> producing a true square wave as we might've for a true sine or sawtooth
> wave. The result is unchanged though- this is clearly the limit of the format.
Buy a good book on Discrete Signal Processing. It'll prove you mathematicly that
if you sample a 22.05 kHz sinewave at 44.1kHz, you'll get a digital signal that
represents this sinewave. It doesn't represent a square-wave at all. Do a
z-tranformation on a sin-wave and go back to the norma domain (inverse
z-transformation). It'll give you a sine-wave. Not a square-wave.
> >> A steep sine wave simply cannot be accurately represented at a 44.1kHz
> >> sample rate.
> >>
> > Not sure what this means.
>
> I mean that you can't draw a *particular* smooth line (the intended
> waveform) when you only have two points on that line (samples with their
> centre points 1/44.1 ms apart). Any line you draw is an approximation to
> what might have been intended. In the acoustic domain, we can theorize that
> a sine curve would be a good bet, but there even a few ways we can draw
> that through two points.
AD and DA conversion is NOT taking samples and connecting lines. And that's
where you go wrong. It's a mathematical transformation of the signal. And yes
(in theory) to accuaratly sample (transform into the discrete -digital- domain)
a sinewave of f hertz, you have to sample it at 2x f hertz. Like Colin and I
pointed out in another threath, the sampling time should be infinitive small
(called epsilon in mathematics).
Another problem is that a infinitive steep low-pass filter is required at f Hz
for the input and the output.
Cheers,
Ralph -> digging very deep into his brains.....
--
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Ralph Smeets Functional Verification Centre Of Competence - CMG
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Mobile: (+33) (0)6 82 66 62 70 38240 MEYLAN
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"For many years, mankind lived just like the animals. And then some-
thing happened that unleashed the powers of our imagination: We learned
to talk."
-- Stephen Hawking, later used by Pink Floyd --
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