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From: mhorne@ka7axd.WV.TEK.COM (Michael T. Horne)
Newsgroups: comp.dsp
Subject: Re: Pitch shift / offset and FFT
Message-ID: <4730@orca.WV.TEK.COM>
Date: 27 Sep 89 22:18:19 GMT
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In a recent article by Steve Wasserman...

>If you have a 1000 Hz sine wave and an 1100 Hz sine wave, and you ADD
>them, you will not get a 100 Hz harmonic, but rather the two
>frequencies will BEAT together at 100 Hz.  The perceived effect (in
>sound, at least) is a 1050 Hz signal that rapidly gets changes volume.
>(Actually, I'm not totally sure what you'd hear with 1000 & 1100.
>But, if the frequencies were closer, say 1000 and 1005, you would
>certainly be able to hear the two beating.  Accurate tuning of musical
>instruments is possible by listening for this beating against a
>properly-tuned standard.)  Anyway, if you looked at 1000 Hz PLUS 1100
>Hz on an oscilloscope, you would see 1050 Hz modulated by a 100 Hz
>envelope.  By the nature of the Fourier Transform, nothing in this
>signal would correlate with 100 Hz.  

When you add two sinusoids together, you get exactly that: the sum of
two sinusoids.  Any apparent beating between two (or more) added 
sinusoids is purely a perceptual effect.  In the case of hearing a
beat between two summed sinusoids, the ear is acting as a mixer which
detects the sum/difference signals as well as detecting the base
signals.  Looking at the sum of two sinusoids on a `scope may lead one
to believe that somehow the sum of the two signals has yielded two
(or more) new, different signals.  This interpretation may seem valid,
but nothing magical is happening: you're only seeing the result of two
sinusoids being summed together, not a mixing of the two.

>-- 
>swass@apple.com

Mike Horne
mhorne@ka7axd.wv.tek.com