Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!wuarchive!brutus.cs.uiuc.edu!apple!wass
From: wass@Apple.COM (Steve Wasserman)
Newsgroups: comp.dsp
Subject: Re: Pitch shift / offset and FFT
Message-ID: <4384@internal.Apple.COM>
Date: 26 Sep 89 22:48:41 GMT
References: <89264.171306P85025@BARILVM.BITNET> <9520001@hpsad.HP.COM> <1787@draken.nada.kth.se>
Organization: Apple Computer Inc, Cupertino, CA
Lines: 35

In article <1787@draken.nada.kth.se> h+@nada.kth.se (Jon W{tte) writes:
... much stuff deleted ...
>
>Also, how about an algorythm that reduced frequency mixing interference
>rendundance from the FFT ? Or is that already taken care of ?
>I.e. if you have one 1000 Hz sine wave and one 1100 Hz sine wave, you'd
>also get one 100 Hz harmonic (and probably a 2100 Hz harmonic as well ?)

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.  

Essentially what I'm saying is that linear superposition applies and
that when you linearly add to frequencies, that is exactly what
happens in the frequency domain - they are added to the original
spectrum and no harmonics are created.

It is a different situation, of course, if you MULTIPLY the two
signals.

1000 plus 1100 looks different than 1000 plus 1100 plus 100 plus 2100,
so it is not really redundant information.


-- 
swass@apple.com