From: kong@leland.Stanford.EDU (Kong Kritayakirana)
Subject: CD Sound (again?)
Organization: DSG, Stanford University, CA 94305, USA
Date: Mon, 28 Dec 92 05:21:09 GMT

From: vanz@tragula.equinox.gen.nz (Martin Nieuwelaar)
 
>Say you sample at 44 KHz.  The maximum theoretical limit of frequency
>you can capture is half of this, 22 KHz.  However, at this rate there
>are only two samples per cycle.  With two samples per cycle, a sine
>wave will sound the same as a square wave.  Surely this is not hi-fi?
>Suppose you say that you cannot hear this high a frequency.
>Well, at 11 KHz, there will be 4 samples per waveform.  How close
>to a pure sine wave can you get with 4 samples?  By looking at it,
>not very.  I'm not sure how noticable the difference in the sound is.
>I guess it wouldn't be difficult for someone with a computer with
>reasonable sound capabilities to try this out.
 
Given that you have a waveform (any waveform) that's periodic with 
fundamental freq of 11kHz. And if you don't have "super ears" to hear beyond 
20kHz. They all will sound the same if the amplitude of the fundamental 
freq (11kHz) is the same for the harmonics are all beyond 20kHz.
 
From: andrey@cco.caltech.edu (Andre T. Yew)
 
>Let's go through a little proof of why 2 points is enough
>(it really isn't -- you can retrieve information that has
>just below half of your sampling frequency;  as an example, point-
>sample a sine wave at exactly twice its frequency and look
>at its Fourier transform).
 
Be VERY careful when you talk about sampling a sine wave with the 
sampling freq which is EXACTLY twice the freq of the sine wave. The 
issue is complex and has to do with the PHASE of that sine wave as well. 
Strictly speaking, you CANNOT always recover a signal that's exactly 
half the sampling freq. Send me mail for more explanation.
 
[a darned good attempt to explain sampling & recovering deleted]
>        Here's a piece of party trivia that some might feel
>would put a damper on the wonderful sampling theorem:
>a bandlimited signal is not timelimited.  And vice-versa.
 
True. But for practical purposes, this is quite ....um.... not of any 
consideration, and for good reasons too.
 
>        A much better explanation of this is found in the
>book by Oppenheimer, somebody, and Young, called, I think,
>_Signals and Systems_.  It's a red book.
 
Oppenheimer and Schaefer (forgive my spelling) "Discrete Time Signal 
Processing"
 
From: jj@alice.att.com (jj, curmudgeon and really disguted scientist)
 
>It's this loss of resolution that I suspect is brought on by
>non-normalized digital transfers in the recording chain that
>annoy me.
 
That bugs me too. If we normalize digitally so that MSBs of 16 bit 
signals are used, 16-bit can give us wonderful sounding recordings.
 
From: chased@rbbb.Eng.Sun.COM (David Chase)
 
>When people say "oversample", I believe that all they mean is to
>repeat the sample value 2, 4, or 8 times.  I don't think they
>interpolate, though they might.  This sounds crazy, but it isn't.
 
Nope. They insert 1, 3, or 7 zeros between samples (corresponds to 2, 4, 
and 8 times oversampling respectively) and then pass the zero-inserted 
signal through a digital low pass filter that interpolates nicely 
between the points.
 
From: myers@hpfcso.FC.HP.COM (Bob Myers)
 
>Once more, with feeling: THERE IS NO DIFFERENCE BETWEEN A 22 kHz SINE WAVE
>AND A 22 kHz SQUARE WAVE UNTIL YOU CONSIDER COMPONENTS AT 66 kHz AND ABOVE.
>If you think you can hear that high, fine.  44.1 kHz sampling can reproduce
>ALL components up to 22 kHz EXACTLY.
 
All components up to BUT NOT INCLUDING 22.05kHz signal.
                     ^^^^^^^^^^^^^^^^^^^^^^^^^^
----------------------------------------------
Kong Kritayakirana  (kong@leland.stanford.edu)
Remotely reading and posting to rec.audio from
a nice beach somewhere in south pacific.  Damn
the technology that helps  us to get in touch.
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Newsgroups: rec.audio