Message-ID: <33DCE1CE.53A9@webworldinc.com>
Date: Mon, 28 Jul 1997 13:15:43 -0500
From: Christopher Weare <cweare@webworldinc.com>
Reply-To: cweare@webworldinc.com
Organization: Arboretum Systems
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Newsgroups: comp.dsp,,comp.speech
Subject: Re: Basic question regarding CD quality audio.
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Sakari Aaltonen wrote:
> 
> In article <ebohlmanEE0Cu9.DyB@netcom.com>,
> Eric Bohlman <ebohlman@netcom.com> wrote:
> >Ashok Ramasubramanian (ashok@dspse.com) wrote:
> >: Hey People,
> >:      I have a basic question regarding CD quality audio. I read somewhere
> >: that CD audio is sampled at 44KHZ, now the highest frequency that the
> >: human ear can detect is 20KHZ. Even this is barely audible. I connected
> >: a signal generator to a speaker and tried all tones , sweeping my
> >: frequency from 0 to 20KHZ, beyond 16KHZ, the sound was pretty hard to
> >: bear(The kind that drives the insects away). SO my question is :if 16KHZ
> >: is the most comfortable frequency , and applying the sampling theorem we
> >: need only 32 KHZ for good quality CD Audio. What is the point in wasting
> >: the extra 12 KHZ of digital bandwidth?
> >
> >The reason is that there's no such thing as a perfect low-pass filter.
> 
> The sampling theorem is often understood to say that if the highest
> frequency in a signal is f, then, if you sample at a rate higher than
> 2f, all is well. That is, you can reconstruct the original signal
> from the samples. As far as I know, however, the reconstruction
> needs an infinite number of samples. So, because a CD cannot contain
> an infinite number of samples, I would say the sampling theorem
> is not directly applicable...

This is not what the sampling theorem says.  If you needed an infinite
number of samples to represent a signal than it would not be band
limited.  The sampling theorem says that if the signal is band limited
then you can capture all the information in the signal by sampling at
just above twice the highest spectral component of the signal.


Reconstruction of the signal is a different matter and idealy involves
the use of an infinitely long acausal filter.  Perhaps this is what you
were aluding to.


Chris Weare
Arboretum Systems
