From: jfw@neuro.duke.edu (John F. Whitehead)
Newsgroups: rec.music.phish
Subject: Re: DAT & CD by the numbers / Whipping Post / Tape gens
Date: 25 Jan 93 23:37:43 GMT
Organization: Duke University; Durham, N.C.

In article <1993Jan24.005731.4252@uvaarpa.Virginia.EDU> AGRABINSKI@sc9.intel.com writes:
>First, to contextualize some concepts in the DAT vs CD technical 
>discussion.
>
>Sampling rate: 44.1 kHz (CD) vs 48 kHz (DAT).  Because of the vagaries 
>of DSP (which I'll admit to understanding very little about, apart from 
>this little nugget), the reproducible frequency is half the sampling 
>rate.

The "Nyquist frequency" is the minimum frequency you can sample a wave
at in order to determine the wave's frequency.  It must be no less than
twice the frequency of the wave.  So to determine the frequency of sound
that goes up to 24KHz, you must sample it at least at 48KHz. 

>Ergo, CD goes to 22kHz, DAT to 24kHz.

Almost -- they get cut off a little below that because filters aren't
perfectly "brickwall" (they cut frequencies off slowly).

>Conclusion: sampling rate has no effect 
>on how good it sounds.  

On most stereo systems, yes.  A higher sampling rate, however, allows one
to use a less severe filter (to cut off frequencies above 20KHz).  A much
higher sampling rate -- several times above 24K instead of just twice --
would improve the sound by allowing more accurate wave analysis.  But
because of the current limits of technology, 48K is the practical limit,
and the difference between that and 44.1K is negligible.

>Data word size: 16 bit (CD) vs 24 bit (DAT).  

No, both CD and DAT use 16 bit.  Some professional gear (mostly signal
processors) use 18 or 20 bits, but even then that's just to avoid
round-off errors since they have to go back to 16 bits for CD or DAT. 

>The 8 additional bits are 
>less significant than the Least Significant Bit (LSB) of the CD.  Each 
>additional bit adds half as much resolution as the previously more 
>significant bit (ie, the MostSB is half; the 2nd MSB is a quarter; etc).  
>2^16 = 65536, 1/65536 = 0.00001526, 65535/65536 = 0.99998474 => 99.9985% 
>of the sound is conveyed in the first 16 bits.  What you get for the 
>additional 8 bits is most of the remaining 0.001526%.  Big deal.  
>Conclusion: data word size has even less of an effect.  

Wrong!  The data word size is very important -- that's what gives the
music its resolution.  A 16-bit recording has a theoretical dynamic
range of 96 dB -- in practice it is usually more like 90-94 dB because
of dithering and noise.  At 20 bits, one could record a dynamic range
of 120 dB, and at 24 bits a range of 144 dB!  This not only means your
recordings would be able to have a much broader range of dynamics (the
difference between the softest and loudest parts), but also that you
could be less concerned about overloading your tape.  Most people are
currently unable to get 96 dB out of 16 bits because they have be wary
of overloading (and the units have residual noise).

-- 
 ________________________________________________________________________
|   John      jfw@neuro.duke.edu          Duke University Medical Center |
| Whitehead   jfw@well.sf.ca.us           Department of Neurobiology     |
|________________________________________ Durham, North Carolina ________|
Newsgroups: rec.music.phish