Via: uk.ac.sheffield-city-poly.ash; Mon, 5 Oct 1992 14:11:17 +0100
Organization: Sheffield Hallam University
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Newsgroups: bit.listserv.emusic-l
Date:         Mon, 5 Oct 1992 14:12:14 GMT
Reply-To:     M.Rootes@sheffield-city-poly.ac.uk
From:         Martin Rootes <M.Rootes@SHEFFIELD-CITY-POLY.AC.UK>
Subject:      Re: 8/16 bit
Comments: To: EMUSIC-L@AUVM.AMERICAN.EDU

Martin Roth writes:-
> ............................................................. Sure 16 bits
> steps are a better approximation to the original, but WHY? Sampling Therem
> states that disortions caused by the sampling in discrete time steps causes
> only disortions higher in frequency than half the sampling frequence. So if
> you add a low-pass after the DAC (what is done allways), you have NO
 distortion.
>
> If I think about it, I believe that Sampling Theorem is true for discrete-step
> sampled continuous signals, but assumes continous values at each step.
> Is there a sort of extension to reduce the single sample steps to a finite
> number of levels? How does that affect frequency response?

The sampling theorem you refer to only concerns itself with the highest
frequency that can be represented and the phenomona of quantisation noise. A
low pass filter is an absolute necessity on the output of a DAC, otherwise
quantisation noise would be present (which is higher than half the sampling
frequency). The number of bits in a sample does not affect the frequency
response but the Signal to Noise ratio. The S/N ratio is affected because if a
system has less values to respresent the original analog system errors will
creep in, which will be perceived as noise. If you have an 8 bit system the
level of a signal at any point can only be represented by 1 of 256 values, any
signal level which falls anywhere between two of these values (a very common
event) will therefore be incorrectly represented. This discrepency is
effectively noise, and is 1/256 of the maximum signal level for an 8bit system.
Offhand I can't remember what this is in term of db, but it is very bad and gets
even worse for complex waves. 16bit systems have 65536 discrete levels, and a
far better S/N ratio (over 100db). For a thorough explanation of this and other
related matters see Hal Chamberlin's Musical Applications of Microprocessors.

> To illustrate my questions, imagine a 2-level digitised sound at an extremely
> high sampling rate. I'm sure it can not reproduce anything like music, but
> why? How can the Sampling Theorem be extended to take into account the
> discrete signal levels?
See above.

> Could _this_ be the diffrerence between a good vinyl record and a
> cd (I know some people who state that vinyl, on a high end
> player of course, is still a lot better than top-quality cd).
I often doubt what Hi Fi buffs say about pieces of equipment etc, there are
many reasons why records sound different from CDs. Theorectically a perfect
record player will be more accurate than a perfect 16bit CD, as record players
are continuos analog and so do not suffer from quantisation and digitisation
noise. However, there is no such thing as a perfect record cutter, let alone
a perfect record player, perfect amp and perfect speakers. CD's probably give
a more accurate output than even top of the range record players, but some
people prefer the softer (less high frequencies) sound of records.

Martin.





>
> - -Martin
> _______________________________________________________________________
>       _   Martin Roth                Martin Roth    ETHZ, ips, RZ F16
> |\  /|_)  Mail: roth@ips.id.ethz.ch  Sandacker 14   g 01/256 55 68
> | \/ | \                          CH-8154 Oberglatt p 01/850 32 75
>           (Eng. Comp. Sci. ETH)      Switzerland    (F-)emails welcome!
> - -----------------------------------------------------------------------
>
>
> ------- End of Forwarded Message
>------------------------------------------------------------------------------
Martin Rootes - Senior Systems Programmer/Analyst, Sheffield Hallam University
Email :         M.Rootes@scp.ac.uk
Disclaimer:     Sheffield Hallam University has no opinions, the ones above
                are mine.
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