From: jj@alice.att.com (jj, curmudgeon and shouter of trvth)
Newsgroups: rec.audio
Subject: Re: Digital vs Analogue, Yet Again!
Date: 28 Jan 93 18:46:05 GMT
Article-I.D.: alice.24739
Reply-To: jj@alice.UUCP (jj, curmudgeon and shouter of trvth)
Distribution: na
Organization: NJ State Home for Bewildered Terminals

In article <1993Jan28.012337.15017@scott.skidmore.edu> jreiser@scott.skidmore.edu (Jason Reiser... Asleep) writes:
>The following is an excerpt from The Absolute Sound,
>July/August '92 by Gerard Rejskind.
Oh, boy oh boy.  Someone is posting THAT bit of abject
misttakenness!  Unbelieveable.

:"DYNAMIC RANGE PROBLEMS:
:	Digital's biggest selling point is its wide dynamic range.
:Certainly it is true that most CD's do not suffer from ticks and pops
:(unless they are mistracking, a common phenomenon that usually comes
:as a shock to new CD owners).  In fact, digital systems have quite
:poor dynamic range.  The usual claim of over 90 dB of dynamic range is
:based on a common mathematical blunder, coupled with what may be
:outright fraud.
Well, that's a good way to start. I think he's left himself open
to a lawsuit there, if somebody cared enough about such
ravings to be truly concerned.

:	The formula for calculating the theoretical maximum dynamic
:range of a digital system is well known.  It is:
:	20 log (2^b - 1)
:where b is the number of bits in the system.  Since the CD uses 16
:bits, we can calculate the dynamic range:
:	20 log (2^16 - 1) = 96.33 dB
Very true.  Now, you left a few things out. But what?

:The calculation ignores the fact that all 16
:bits are not used for signal data.
A lie.  I have CD derived data on this machine, and it uses all
16 bits for data.

: The last bit is used as a parity
:check (which alerts the error correction circuit that something is
:wrong with the data), and so we should do the calculation with only 15
:bits:
:	20 log (2^15 - 1) = 90.3 dB
A completely factual untruth, fabricated of whole nonsense, and
easily provable and testable by the use of any handy
workstation with an SPDIF interface.  The CD uses all 16 bits for
data. There is no parity bit included in the 16 bits.  On the
disc, there is much MORE protection, specifically 14 bits are
used to encode each 8 bits.  In light of this, parity checking
is theoretically as well as factually moot.  <Those who wonder
are encouarged to study error detection and correction. It is
well established that all error detection and correction is
best done at one shot, in order to recover all available information.>

:	This is still very good, but there is a problem: It expresses
:the peak-to-peak value of the noise.  The usual way we measure noise
:is by its root mean square value.  To convert, we need to subtract:
:	20 log (2 x SQR(2)) = 9.03 dB
Another mistake.  "its root mean square value" assumes some
model of a signal, in this case a sine wave.  As we all know,
"nobody listens to a sine wave".  As we also know, this is ignoring
the issue that one must consider the peak-peak value of not
only the music, but also the NOISE, assuming the noise is 
uniformly distributed, one forgets another factor of 10(log10(1/12))
here, adding back about 10.7 dB to the 9.03 db.  Now, using
some sensible mathmatics, we seem to have, oh about, lessee,
96 +1 or 97!! dB.  That's quite a difference from the
nonsensical value of 81dB that this turkey provides.  

:	We are now down to about 81 dB, not all of which is usable,
:because digital has a "hard ceiling" that you can't cross without
:disastrous distortion.  If we leave an extra 8 dB of headroom, we are
:now down to 73 dB, considerably less than we can obtain with a modern
Ok, using the 2.5dB I measure on most CD's  (peaks in the range
of +- 25000), that takes us down to about 94dB or so.

That's well over what anyone gets with Dolby (tm) or
most any other analog noise reduction system, and it's NOT
dynamic, it's absolute.

:Even so, the bottom
:part of the dynamic band is not usable because low level signals
:suffer, in nearly all players, from severe distortion. 
This is true for SOME cheap players, but certainly not all.

:This can be
:reduced considerably by the proper use of dithering (the deliberate
:addition of abalogue noise to the signal), but a simple instrument
:test confirms that only the best players can reproduce a sine wave at
:a level of -60 dB as anything but a caricature of the original.
Curiosly enough, putting my cheap sony on the AA501, I get about
88dB, which is a whole lot better than 60dB.  Additionally,
dithering is a RECORDING operation, not a DAC operation, showing
the thorough failure of this author to misunderstand the technology
in any way, shape, or form.  The author also shows his or her
weakness in understanding by commenting "caricature...", not
having (quite obviously) at what one gets at -60dB in
an ANALOG system (i.e. you'd have a hard time even seeing the
waveform, let alone calling it a caricature).

:	So why do CD players seem dynamic range of over 90 dB?  This
:figure is based on the (deliberate?) confusion of two concepts. 
Well, if there's any confusion here, it's not on the part
of the CD player, or the manufacturer.

:Turn
:off the signal in an analogue system, and you can read the system's
:actual noise. 
False.  You are left with the system's IDLE noise, but you
are missing all the dynamic noise present in an analog system.

:Do the same in a digital system, and you are left with
:nothing at all. 
False again, you are left with a white-noise source of +-1/2 
the smallest step in the DAC.  Sending '0's to a DAC in the
absense of input signal shows a failure to use recording dither
correctly.  The only time one sends '0's is when there is no
DATA present, i.e. when no CD is being played.

:Noise measurements of CD players usually express
:nothing more than the residual noise of the analogue section. 
This is another complete fabrication based on a total misunderstanding
of the very basics of digital audio technology.

This example of an 'expert' article shows the depths to which
the audio community in the USA has sunk.  Luddism and misinformation
like that refuted above (for references to this refutation, go look
at Jayant and Noll's book on Coding, Taub and Schilling on
communication, Shafer's books, Rabiner and Gold, heck there
are dozens of books out there to explain this.) are what
runs rampant through the US audio community, to its great
disadvantage and slow but sure disappearance.
-- 
Copyright alice!jj 1993, all rights reserved, except transmission by USENET and like facilities granted. Said permission is granted only for complete copies that include this notice. Use on pay-for-read services specifically disallowed.
---------
Member HASA - Athiest Scum Division
"Extremism in the defense of liberty is no vice" - AuH2O for President