charles@sunybcs.UUCP (Charles E. Pearson) (06/20/84)
>From rocksvax!dave Tue Jun 19 21:10:42 1984
Subject: Re: CDs: why no square waves?
No you missed the point. Look in a communications theory book what
components make up a square wave: it consists of a sine wave at
nearly the full amplitude of the square wave + 3rd harmonic at 1/3
amplitude + 5th harmonic at 1/5 amplitude + 7th harmonic 1/7
amplitude..... infinitely. All arbitrary waveforms are made up from
sums of sine waves. Nyquist says that any arbitrary wave can be 100%
reproduced if you sample at a rate 2*the highest SINE wave it consists
of. No device can sample at 2*infinity not even an analog device.
What that says of a CD is the following a 22 Khz square wave comes out
a 22 Khz sine wave. Those differences people claim to hear usually are
caused by intermodulation effects with some system non-linearity
causing lower frequency signals to be generated. The next meaningful
SINE component of a 22 Khz square wave is 66Khz at 1/3 the amplitude.
Unless that group of people can also detect 66 Khz singly then the whole
argument is bull-shit.
At the end of this message are examples of bandpassing a square wave at
each harmonic. That "ringing" you see is not really that at all. If you
eliminate unheard components and sample at 2X rate you can reconstruct
exactly what went in. For those that need numbers:
first waveform is that of 22Khz sq wave sharp low passed below 22Khz
second waveform is that of 7.3Khz "" (22/3)
third waveform is that of a 4.4Khz "" (22/5)
forth waveform is that of a 1.2Khz "" (22/19)
and the fifth is that of a 1.0Khz "" (22/21)
If you have a real plotter try plotting series of this formula:
y = SIN(x) + 1/3*SIN(3x) + 1/5*SIN(5x) + ... 1/odd*SIN(oddx)
The bigger odd is the closer to a real square wave you get, the
harder it is for your plotter to plot.
As for keeping records clean and buying more expensive turntables, I can
only say I bought records so that I could record them onto cassettes. I would
then play the cassettes, because they would go unattended for about 45 mins.
The album need attention every 22 mins plus the static zapper and discwasher
treatment, etc, etc. Contrast that with CD at 72 mins and rare cleanings
plus same or better fidelity in the ranges it counts in. After one playing
those 66Khz and greater vinal modulations will have been altered.
For approx the same money I get a media that eventually will fit in
my walkman, car and home system. I will not need to record the album
to take it skiing with me. So take you bloody analog prejudices off our
net. Sheffield labs ought to eat all those "Stamp out digital madness"
tee-shirts they sold now that they are in the CD business!!!
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end of quote.................
You have already admitted defeat, you will take about 2 years to
realize it, though.
You have attempted to generate a square wave from sine waves.
This is the analogue approach.
So you are an analogue supporter yourself.
You missed the fact that this approach will produce a proper
(and flat) square wave as the number of terms approaches
infinity. (Just like a Taylor Polonomial approaches an
alternate expression of the original function.)
The digital approach would produce the flat square wave from the start.
Funny how people will argue for hours, never knowing that they are
really arguing the same point.
Welcome back to the fold.
Charles E. Pearson
UUCP: {allegra, seismo}!rochester!rocksvax!sunybcs!charles
decvax!watmath!sunybcs!charles
ARPA & CSNET: charles.buffalo@rand-relay
Physical: University Computing Services
4250 Ridge Lea Road
room 28
SUNY Center at Buffalo
Amherst, NY 14226
P.S. As for Sheffield...
Quoted from one of their people...
"The CDs allow us to keep producing the analogue disks."
In other words... What P. T. Barnum wants P. T. Barnum gets.