From: kong@leland.Stanford.EDU (Kong Kritayakirana)
Subject: Bogus Arguments about Digital Audio
Organization: DSG, Stanford University, CA 94305, USA
Date: Thu, 28 Jan 93 05:49:37 GMT

From: jreiser@scott.skidmore.edu (Jason Reiser... Asleep)
 
>Wouldn't it be nice if CD players were actually capable of anything
>approaching 95dB dynamic range!
 
Yes, it would. They actually CAN do a little better than that.
 
>But, sadly they fall quite short of this,
 
No, they don't. 95dB of dynamic range is definitely possible.
 
>and the numbers quoted throughout the industry are strictly
>bogus!
 
No, they are not.
 
>The following is an excerpt from The Absolute Sound,
>July/August '92 by Gerard Rejskind.
 
Pseudo-technical with a lot of faulty information, let me tell you.
 
[stuff deleted]
>The usual claim of over 90 dB of dynamic range is based on a common
>mathematical blunder,
 
Seems like the writer of this article knows nothing about DSP or the effect 
of quantization on dynamic range and signal to noise ratio. So it is not his 
mathematical blunder, but rather his ignorance on the subject he addressed.
 
>        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.
 
WRONG. The formula is: Dynamic range (dB) = 6.02*b+1.76  So for CD, the 
theoretical dynamic range is 98.1dB for 16 bit data. Email me if you want 
references to this formula. They're tons. Not one of them was written by 
"subjective" audio reviewers.
 
>Since the CD uses 16 bits, we can calculate the dynamic range:
>        20 log (2^16 - 1) = 96.33 dB
 
Right Number --> Wrong Formula --> Meaningless Result
 
>The calculation ignores the fact that all 16
>bits are not used for signal data.  The last bit is used as a parity
>check (which alerts the error correction circuit that something is
>wrong with the data)
 
CD uses 8-to-14 data interleaving/error correction. You actually get all 16 
bits to use to encode the signal. Another flop by this TAS writer.
 
>and so we should do the calculation with only 15
>bits:
>        20 log (2^15 - 1) = 90.3 dB
 
Wrong Number --> Wrong Formula --> Meaningless Result
 
>This is still very good, but there is a problem: It expresses
>the peak-to-peak value of the noise.
 
90.3 dB peak-to-peak noise??? Tell him to go read a DSP textbook, will you?
 
>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
>        We are now down to about 81 dB,
 
Wrong Formula + Serious Misunderstanding --> Meaningless Result
 
[phony discussion about very complicated digital headroom issue deleted]
>Even so, the bottom part of the dynamic band is not usable because low
>level signals suffer, in nearly all players, from severe distortion.
 
He's probably looking at datasheet of circa 1984 DAC chip to arrive at this.
 
>This can be
>reduced considerably by the proper use of dithering (the deliberate
>addition of abalogue noise to the signal),
 
WRONG. Dithering is noise added to make sure that the quantization noise 
becomes uncorrelated with the digital signal to avoid noise exhibiting 
behavior like harmonic distortion. And dithering does not have anything to 
do with low level linearity. Apples and oranges got mixed up here.
 
>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.
 
I guess the "simple" test instrument is the one at fault then.
 
>So why do CD players seem dynamic range of over 90 dB?  This
>figure is based on the (deliberate?) confusion of two concepts.
 
The writer definitely has confusion of a lot more than two concepts.
 
>Turn off the signal in an analogue system, and you can read the system's
>actual noise.  Do the same in a digital system, and you are left with
>nothing at all.  Noise measurements of CD players usually express
>nothing more than the residual noise of the analogue section.  Not
>surprisingly, it is usually terrific.
 
Finally he's got a point. It is true that some DACs try to cheat, ie., mute
its output when no digital input is detected. But even if they don't,
the signal to noise ratio is well above 90dB.
 
>ANALOGUE PROBLEMS:
>This is the problem that most player designers attack first,
>because most of them know analogue better than digital.  Because of
>price pressure, most companies cut corners wherever they can.  Their
>analogue sections usually contain inexpensive amplifier chips,
>including the venerable (and horribly slow) 741.
 
741 opamp has been dead for years. Most el cheapo CD players use 5532s.
Terrible opamp in my opinion, but still way much much better than jurassic 
741. Again the writer might not have seen any development in integrated 
circuits since 1970 or so.
 
>Such chips will spoil anything,
 
It certainly will. But the point is they are not used in CD player. You find 
them in EE labs for first course in analog electronics.
 
[another conclusion based on ill-informed knowledge on the subject deleted]
 
>Well, what is to be done?  I think we need to speak up,
 
Yes. We say, "Go get a grip on DSP, Gerard."
The article is laid with so much faulty information that it becomes 
quite hard to argue with the writer who knows so little about what he wrote
and stood up to make a "profound" point.
 
>growing acceptation, even in certain audiophile circles, of common
         ^^^^^^^^^^^
         Acceptance. Wonder what TAS editor has been doing lately....
 
>Think about it."
 
I did. But he sure didn't understand DSP well enough to write what he wrote.
 
>                                - Jason
 
This is not a personal attack on you. But hope you get a better idea now 
what digital audio really is. And hopefully you get some idea about quality 
of The Abso!ute Sound's technical editor.
------------------------------------------------------------------------------
Kong Kritayakirana

Newsgroups: rec.audio