From: chased@rbbb.Eng.Sun.COM (David Chase)
Newsgroups: rec.audio
Subject: Re:  CD SOund QUality
Date: 24 Dec 1992 01:43:41 GMT
Organization: Sun
NNTP-Posting-Host: rbbb

In article <vanz.029i@tragula.equinox.gen.nz> vanz@tragula.equinox.gen.nz (Martin Nieuwelaar) writes:
>Say you sample at 44 KHz.  The maximum theoretical limit of frequency
>you can capture is half of this, 22 KHz.  However, at this rate there
>are only two samples per cycle.  With two samples per cycle, a sine
>wave will sound the same as a square wave.  Surely this is not hi-fi?

Another poster has already gone sinc-convolution song-and-dance.
If you followed that, then I'll add the bit about oversampling.

>I haven't introduced oversampling, as I'm still not too sure what it
>is.  If someone could tell me if what I think is correct, is
>correct I'd be pleased.

When people say "oversample", I believe that all they mean is to
repeat the sample value 2, 4, or 8 times.  I don't think they
interpolate, though they might.  This sounds crazy, but it isn't.

On playback, if you do straight sampling, all your 44Khz wide (+/-
22Khz) boxes are adjacent.  At "23Khz", what you hear is some other
part of your signal, all twisted up, and not what was at the original
23Khz.  To get your signal and no weird noise from the box centered at
44KHz, you need a "brick wall filter" at 22Khz.  Problem is, brick
wall filters are kind of hard to build in analog circuits, and they
tend to involve other compromises that you didn't really want to make.
(In practice, you don't need a brick wall -- you just need it to be
many decibels down past 22Khz).  Oversampling puts more space between
the boxes.

Oversample by 2 (88Khz) and you have a 44Khz gap to work with.  (One
box from -22 to +22, another from +66 to +110, etc.)  Oversample by 8,
and you have a couple of octaves to work with (22 to 330Khz).  What
this means is that your filter does not need to be quite so severe,
and you can make fewer compromises.  I'm not really sure why someone
would go as far as x8 oversampling, but (if it is not just marketing)
it might have something to do with high frequencies screwing up your
audio amplifier (but I must point out that I am very nearly clueless
on this -- it's been almost 13 years since I studied transistor
amplifiers).

On the recording end, a higher sampling rate helps because you want to
avoid recording aliases of high frequencies.  The recorded signal must
be bandlimited to very low levels above 22Khz, or else you will get
aliasing (conceptually, your frequency boxes are clipped at 22Khz and
pasted on again starting at 0.  Think of applying a strobe to a wheel
spinning a little bit faster than the strobe flashes).  Once again,
building an analog filter that will do that well without screwing up
the sound nearby (say, at 20Khz) is difficult.  On the other hand, if
your recorder oversamples by 2 (for real, this time, and not one
sample repeated twice), you only have to bandlimit your signal to
44Khz.  What this means is fewer compromises in your analog filters.

Now, after the sound has been recorded at 88Khz, you digitally process
it down to a sampling rate of 44Khz.  You can do more interesting
things with digital signal processing, so you get better filtering (I
think you can build a real brick wall filter, for instance).  I read
recently (NY Times, within last 4 months) that some company had
started producing equipment that would do this (for professional
recording, I believe).  I think they even got a patent on it, which is
sort of sad, seeing how it fails the "obvious" test (I thought
everyone did this already).

Clear as mud, right?  I've got multiple books that purport to explain
this, if you want references, but you had better be prepared for a
little bit of math.

David Chase
Sun
Newsgroups: rec.audio