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From: davet@cbnewsj.att.com (Dave Tutelman)
Newsgroups: comp.music,rec.music.synth
Subject: Re: Looking for Equations for Sounds
Message-ID: <1991Jan10.120734.1710@cbnewsj.att.com>
Date: 10 Jan 91 12:07:34 GMT
References: <278a4f64.4051@petunia.CalPoly.EDU> <10981@jpl-devvax.JPL.NASA.GOV>
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Organization: AT&T Bell Labs - Lincroft, NJ
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In article <10981@jpl-devvax.JPL.NASA.GOV> brad@huey.Jpl.Nasa.GOV writes:
>
>FM is Frequency Modulation, so you modulate f:
>
>	f(t) = A * sin ( 2*pi*( f_0 + df(t) )*t + phi_0 )
>
>f_0 is the carrier frequency
>df(t) is the modulation function
>
>PM is Phase Modulation (not so common as the other two):
>
>	f(t) = A * sin ( 2*pi*f*t + ( phi_0 + dphi(t) ) )
>
>phi_0 is the phase offset of the wave
>dphi(t) is the modulation function

Looks reasonable, but it's wrong.  The equation for FM anyway.
Actually FM and Phase Mod both have the equation you present for
phase modulation.  It's just that the modulation function for the
phase (dphi(t)) is different for the two types of modulation.

   -	Phase mod : as you show it.
   -	Frequency mod : dphi(t) = S df(t) dt

where S represents the integral sign.
Thus, the equation for FM is

	f(t) = A * sin ( 2*pi*f_0*t + ( phi_0 + S df(t) dt ) )

Check out any book on modulation theory.

>-- 
>Brad Hines
>Internet: brad@huey.jpl.nasa.gov

Dave
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