Feedback in FM synthesis

[Magnus Danielson]

From: "Theo" <t.hogers at home.nl>
Subject: Re: Feedback  in FM synthesis
Date: Tue, 8 Aug 2000 00:02:04 +0200

> 
> ----- Original Message -----
> From: Don Tillman <don at till.com>
> To: <t.hogers at home.nl>
> Cc: <synth-diy at node12b53.a2000.nl>
> Sent: Monday, August 07, 2000 4:52 PM
> Subject: Re: Feedback in FM synthesis
> 
> 
> > John Chowning's original patent is FM.  US patent 4,018,121:
> > http://www.patents.ibm.com/details?pn=US04018121__
> >
> > But the DX-7 patent is clearly PM.  US patent 4,554,857:
> > http://www.patents.ibm.com/details?pn=US04554857__
> >
> > I don't know why Yamaha choose to use PM instead of FM.  I would think
> > that FM would generally sound warmer.
> >
> 
> Ok I admit, me stupid and me math is crap.
> Could someone explain this to me:
> (from the dx7 patent)
> "For simplifying the operation circuit by substituting a linear
> multiplication operation
> by a logarithmic addition, the sine wave table 53 stores sine function
> values in logarithm."
> 
> It is easy to see why this is easyer to implement (takes less cells).

OK, good, then we don't have to dwelve too much in those details.

> What I don't get is why the logarithmic addition is the same as a linear
> multiplication.

Well,

         ln(a)    ln(b)    ln(a) + ln(b)
a * b = e      * e      = e

Neither the exp or the ln functions are very cheap thougth. But if you allready
have them one way or another, well... then it is better to reuse the adder than
having a separate multiplier block.

Now, looking at Fig.8 you see the e^x function in block 56, the Log/Linear
converter. The sines values is in log and all other values in log. Smart.
It combines the sinus, user parameter and envelope using two additions rather
than two multiplications.

I'm not up to date with cheap expo-blocks in digital implementations though.

Either way, the DX7 patent is very product specific and form it is seems fair
to say that one could probably cook up some VHDL code to pour into a FPGA to
do an rather accurate emulation. Naturally, once you have done that you are
not far away to do any of the DX series synths and more if you feel like it.
Diffrent operators should easilly allow for themselfs to be assembled.

Cheers,
Magnus