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From: michaelk@tekmdp.UUCP (Michael Kersenbrock)
Newsgroups: net.audio
Subject: Re: Superstition revisited - let's play some math (CD related).
Message-ID: <2116@tekmdp.UUCP>
Date: Fri, 5-Aug-83 16:14:42 EDT
Article-I.D.: tekmdp.2116
Posted: Fri Aug  5 16:14:42 1983
Date-Received: Sat, 6-Aug-83 11:05:04 EDT
Lines: 39

Actually it is time delay that is the "culprit". The "technical" name for
distortion in this domain is "group delay distortion".  You remember my comments
about moving your head 0.3 inches? Those comments are testable, reproduceable
effects. Put your speakers out in a open field (to eliminate effects that 
we are not testing (like reflections)) and put into it a 
1Khz tone or 20Khz tone .  Put a microphone some distance 
from it, with a scope attached (trigger off another -- but stationary --
microphone).  The phase changes such that 360 deg. 
phase shift happpens in about 1100/f feet.  The wavelength of 20Khz is 
about 0.6 inches, and about a foot for 1Khz. When you move your head/microphone 
forward and back 0.6 inches, the 20K changes 360 degrees, the 1Khz 
changes 18 degrees -- it is obvious because the wavelengths are different.  
If it can be easily demonstrated for a SIMPLE test case, it is definitely 
true for a complex case although *identification* of the cause/effects would be 
more difficult.  Now then, what is my real point? It is this: when you
move your head (we are in a field remember, no reflection effects) there
is no perceivable difference, certainly not with 0.3 inches (180 deg. at
20 KHz).  THIS IS BECAUSE THERE IS A CONSTANT TIME DELAY. The different
frequencies PROPAGATE AT THE SAME SPEED (group velocity). 
     The distortion that we are really looking at is called group delay
distortion  -- which means the frequency domain components for a particular
sound-mechanical or waveform-electrical signal don't arrive at the
same TIME in order to produce the same time domain signal that was started
with. Group delay distortion IS related to phase,but is NOT just phase response.
Group delay itself is the *first* derivative of the phase response, and 
group delay distortion (the part you want to be zero) is the *second* derivative
of the phase response. It doesnt matter how much delay you have, just as long
as all frequencies have the same delay (like how far you are from the speakers).
     I seem to recall that at least some if not most of the CD players
use a seventh order filter.  The reason for such a high order is twofold. 
First, they want a sharp cutoff above 20 Khz. Secondly, they want zero
group delay distortion.  Filters with zero group delay distortion have
a very slow amplitude rolloff, and so it takes a high order filter to
accomplish both goals.  There is a great opportunity here for digital-domain
filtering .

Mike Kersenbrock
Tektronix Microcomputer Development Products
Aloha, Oregon