Xref: utzoo comp.dsp:713 alt.emusic:812 rec.music.makers:8580 bit.listserv.allmusic:3603
Path: utzoo!mnetor!geac!torsqnt!tmsoft!becker!bdb
From: bdb@becker.UUCP (Bruce Becker)
Newsgroups: comp.dsp,alt.emusic,rec.music.makers,bit.listserv.allmusic
Subject: Re: Combining samples......
Keywords: Fourier transforms, music
Message-ID: <14808@becker.UUCP>
Date: 9 Jun 90 06:38:06 GMT
References: <wilf.644264995@endor> <1431@marlin.NOSC.MIL> <48870@seismo.CSS.GOV> <1990Jun6.170458.25618@athena.mit.edu>
Reply-To: bdb@becker.UUCP (Bruce Becker)
Organization: G. T. S., Toronto, Ontario
Lines: 62

In article <1990Jun6.170458.25618@athena.mit.edu> tldavis@athena.mit.edu (Timothy L. Davis) writes:
|In article <48870@seismo.CSS.GOV> black@beno.CSS.GOV (Mike Black) writes:
|>I always though combining two samples was not possible in the time domain.
|>If you add two opposite phase sine waves you'll get a null response.  It's
|>necessary to do a Fourier Transform to the frequency domain, add the 
|>amplitudes, and invert the transform.  This will give you twice the amplitude
|>of the original two sine waves (this would seem to be the desired effect).
|>Am I totally off-base in this rather long-held belief?
|>Mike...
|
|I'm afraid you are, Mike.  First of all, the Fourier transform is a linear
|operator: F[a x(t) + b y(t)] = a F[x(t)] + b F[y(t)]. Thus adding in the 
|frequency domain has the same result as adding in the time domain.  Linearity
|holds for continuous, discrete, and mixed versions of the Fourier transform and
|Fourier series.
|
|Second, two opposite-phase sinusoids SHOULD cancel each other.  Have you
|ever played a wind instrument?  While tuning, the rhythmic beating of the
|blended sound of two horns is the result of the sinusoids going in and out of
|phase. When the beating stops, you are in tune (same frequency).  If you are
|more careful, you can play a long note to be both in tune and in phase with 
|another player (w.r.t. a particular point in space), so that the volume of 
|the summed sound waves of your two horns is near maximal.  Of course, there
|are harmonics generated in the horn and the phase difference of the fundamental
|depends on the position of the instruments and the listener and the room 
|acoustics, but my basic tenent remains that the sound pressure levels 
|generated by each instrument can be algenraically summed to give the sound 
|which would be produced by the instruments playing together.

	In yet another instance of the interplay of art
	and technology, I recommend you investigate the 
	work "Still and Moving Lines of Silence in
	Families of Hyperbolas", by Alvin Lucier.

	This piece, composed in 1983, is recorded on
	an album of the same name, on Lovely Records.

	A quote from the record jacket:

	"Still and Moving Lines of Silence in
	Families of Hyperbolas is based
	upon interference phenomena
	between two or moresound waves.
	When closely tuned musical tones
	are sounded, audible beats - bumps
	of loud sound produced as the
	sound waves coincide - occur at
	speeds determined by the difference
	between the pitches of the tones.
	The larger the difference, the faster
	the beating. At unison, bo beating
	occurs. Furthermore, if each tone
	originates from a separate source,
	the beats spin in elliptical patterns
	through space, from the higher
	source to the lower one."

-- 
  ,u,	 Bruce Becker	Toronto, Ontario
a /i/	 Internet: bdb@becker.UUCP, bruce@gpu.utcs.toronto.edu
 `\o\-e	 UUCP: ...!uunet!mnetor!becker!bdb
 _< /_	 "I still have my phil-os-o-phy" - Meredith Monk