From: deanaj@elec.canterbury.ac.nz (A. J. Dean)
Newsgroups: rec.audio.high-end
Subject: Re: Why digitize: some bunk
Date: 12 Nov 1992 03:06:32 +0000 (GMT)
Organization: Electrical Engineering, University of Canterbury, New Zealand
 <01GR2J7I6LKW8ZI27O@csc.canterbury.ac.nz>; Thu, 12 Nov 1992 16:06:40 +1300
 12 Nov 92 16:06:36 NZD
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Originator: tjk@csd4.csd.uwm.edu

Paul Winser (paul@prl.phil.co.uk) wrote:
: For steady-state sine waves, OK. But steady-state sine waves
: (mathematically) carry zero information. Music, on the other hand is by
: definition an information signal and consists of a series of transients
: or events in the time domain. Can you be sure that all non-repetative
: transient audio waveforms can be losslessly represented by 44KHz samples?

Mathematically, yes, as long as your not trying to represent something with
frequency components above the Nyquist limit. That's not saying there aren't
cases where we can hear frequency components above the CD Nyquist limit in
those special cases (neither is it saying that there is!).

: There *is* a difference between the practice of bandlimiting signals in
: analogue and common digital equipment. Consider the response to an
: impulse of very short duration. A band-limiting analogue filter will
: output an initial large excursion followed by a ringing of diminishing
: amplitude. Digital filters for audio are nearly always designed to take
: advantage of the possibilty for mathematically optimal filter design
: that the storage of samples can provide. The output of such filters is
: seen to be a large excursion with *symmetrical* pre- and post-ringing.
: 
: The pre-ringing of the impulse response in the time domain is acausal,
: that is we appear to get an output before the input has arrived.
: Gross Speculation: Might it be possible that our perception mechanisms,
: optimised by evolution for processing naturally filtered sounds, is
: upset by this very un-natural behaviour? Have there been any attempts
: to design digital filters for audio that mimic the response of analogue
: filters to produce strictly causal outputs?

Hmm. Ringing is caused becuase you are chopping away some of the original
signal (if you were'nt there would be no effect of filtering). If you take a
square wave and perfectly brick-wall low pass filter it there will be
ringing because the high frequency components which opposed the ringing are
gone. This leads to the argument that if you chop away 'frequencies' that
you can't hear, then there will be no difference as your ears, being low
pass filters, will see (hear?) the ringing in either case.

To properly represent a sampled signal perfectly, you have to interpolate
using before and after samples stretching to infinity. Thus, each sample of
the 'filled in' parts of the waveform from an oversampling DAC ideally needs
to be computed from ALL the available samples (ideally infinite) in either
direction. A filter (mostly) does not _produce_ ringing, it just takes away
parts of the signal that would otherwise cancel out the ringing. BTW, it is
possible to make analog filters with the same sort of acausal time response
as these digital linear phase FIR things, they are just a bit impractical
especially these days when they are not needed.

But your "gross speculation" bit does make a lot of sense. When we go
limiting a frequency response (however it is done) we start making
assumptions about how and what we hear. Our ears are very good frequency
detectors, using extremely linear (finally, I can use that word when
referring to the ear) mechanical transforms before sensing occurs for most
of what we hear. It is by no means a fourier transform, but I speculate it
mostly obeys the (linear) sum of sinusoids approach we currently use, so
linear filtering will be, for the most part relevant and predictable. Also
the ear is not purely a frequency sensing device, it also has good time
domain properties, possibly allowing it to detect time domain events that
escape our frequency based model. In fact quite likely come to think of it.
And the thing is, when our assumptions break down, all this mathematical
stuff becomes even further from the truth, especially when they break down
in ways we don't realise or understand. Then to top it all off, the
information (roughly 74 Mbits/s per ear) goes into the most sophisticated
neural processor we know of, to be disected in strange and confusing ways. A
lot of that info is lost, and I presume a fair bit is added as well.

But I suppose if everyone thought like that then everyone would have given
up trying to recreate sound perfectly a long time ago. Basically, in answer
to your question, yes!

Antony.