Feedback in FM synthesis

[Don Tillman]

   Date: Tue, 8 Aug 2000 09:29:55 +0200 (MET DST)
   From: Martin Czech <czech at Micronas.Com>

   :::John Chowning's original patent is FM.  US patent 4,018,121:
   :::http://www.patents.ibm.com/details?pn=US04018121__

   In this patent I see the formula:
   e=A*sin(wc*t+I*sin(wm*t))

   I think I is intended as modulation parameter independend from wm.
   If this is the case, this formula describes PM and not FM.

Sure enough.

The Chowning patent shares a lot with his article "The Synthesis of
Complex Audio Spectra by Means of Frequency Modulation", Journal of
the Audio Engineering Society, 1973.  It was republished as chapter 1
of the book "Foundations of Computer Music" edited by Curtis Roads.

In all cases his equation is, as you note, PM.  

But his block diagram ("Music V" notation) in both the article and
the patent is clearly real FM.

So I just asked Julius Smith about this.  Julius is a professor at
Stanford's CCRMA, worked on FM and currently works on a lot of
physical modeling stuff, and he used to play in my rock band.  He said
that at CCRMA they used both FM and PM implementations.

He also said that PM has an advantage because you can use feedback
without it degenerating. 

I get the feeling that at CCRMA they used the phrase "FM" in a generic
way to mean any situation where one digital oscillator is driving
another.  But I'm really suprised that none of the papers that I've
seen mention the difference between FM and PM.

Of course you know what this means; us analog oscillator builders now
have to come up with a linear through-zero PM input.  Juergen?

  -- Don

-- 
Don Tillman
Palo Alto, California, USA
don at till.com
http://www.till.com