Path: utzoo!attcan!uunet!portal!cup.portal.com!doug-merritt
From: doug-merritt@cup.portal.com
Newsgroups: comp.sys.amiga
Subject: Re: Sampling at 29KHz (long)
Message-ID: <5872@cup.portal.com>
Date: 24 May 88 17:02:26 GMT
References: <2845@polya.STANFORD.EDU> <734@eos.UUCP> <53788@sun.uucp> <5637@cup.portal.com> <3854@cbmvax.UUCP>
Organization: The Portal System (TM)
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Joe Augenbraun writes:
>I've had a couple of questions that I've been meaning to ask an expert. :-)

Thanks for the smiley face; I was only kidding about being an expert!

>The top waveform (let's say) is an 18 KHz signal and the lines underneath
>it are the 44 khz sampling signal used by a CD player:
>[ waveforms deleted ]

The junk that you're seeing in your example is due to 26Khz and 62Khz
aliasing. With a sampling rate of A of a sine of frequency B, you'll
always get two aliased components of frequencies A-B (here 26Khz) and
A+B (62Khz).

This isn't really a problem, since even the 26Khz frequency is beyond the
range of human hearing. You could look at it as though your ear is imposing
a low pass filter on the incoming signal, with a cutoff around 20Khz. If
you filter your example waveform through a 20Khz lowpass filter, you'd
get a nice clean 18Khz signal out of it.

As I said in the other posting, the other way (besides a high sampling rate)
to get rid of unpleasant aliasing is to randomize your sampling frequency,
which distributes the aliasing into low level white noise.

>I know that in theory a sampled signal should be recontructed using some kind
>of funny exponential, but I assume that this is real hard to do in real time.

The "funny exponential" you're referring to is simply one in the domain
of complex numbers, and happens to be equivalent to sines and cosines.
The mathematics of sampling theory, Fourier transforms, etc, can be
phrased either in terms of trigonometry (sines and cosines) or of complex
analysis (complex-domain exponentials). It's exactly the same thing either way.
See Euler's theorem in an algebra book to see why.
	Doug
--
      Doug Merritt        ucbvax!sun.com!cup.portal.com!doug-merritt
                      or  ucbvax!eris!doug (doug@eris.berkeley.edu)
                      or  ucbvax!unisoft!certes!doug