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From: gregr@tekig1.UUCP (Greg Rogers)
Newsgroups: net.audio
Subject: The stuff square waves are made of ....
Message-ID: <1692@tekig1.UUCP>
Date: Sat, 23-Jun-84 17:05:04 EDT
Article-I.D.: tekig1.1692
Posted: Sat Jun 23 17:05:04 1984
Date-Received: Thu, 28-Jun-84 01:02:20 EDT
References: <494@drutx.UUCP> <2546@allegra.UUCP>, <139@brl-vgr.ARPA>
Organization: Tektronix, Beaverton OR
Lines: 23


I'm afraid I contributed to some confusion over the frequency components
of a 20 Khz square wave.  When I referred to a 40 Khz frequency component
I was thinking of a non-perfect "square wave" as might be generated by a 
real world pulse generator, not an artifically created "perfect square wave"
as encoded on a CD test disk.  To set the record straight, rectangular waves,
or periodic pulses, contain a frequency component at 1,2,3,4,...n times the
fundamental frequency (inverse of the repetition rate) in general.  However, 
due to a [sin (x)]/x frequency spectra envelope, the magnitude of the frequency
component is zero at nN times the fundamental frequency, where 1/N is the duty
factor.  Since a perfect square wave has a duty factor of 1/2, (exactly the same
amount of time at its high level and its low level), then its frequency
components at 2f,4f,6f,...2nf are zero.  Thus a perfect 20 Khz square wave has 
no 40 Khz, 80 Khz, etc. components.  However, a real world "square wave" with a
duty factor slightly different than 1/2 will have these components (magnitude
varies with sin x/x function) and this should be taken into account when 
using "square waves" for other types of audio evaluations.  Failure to do this
may lead to some very faulty performance conclusions.  Again sorry if I 
contributed to anyone's confusion.

					Greg Rogers
					Tektronix