[sdiy] interesting patents- Yamaha, Kawai, Ralph Deutsch

[Scott Gravenhorst]

Scott Nordlund <gsn10 at hotmail.com> wrote:
>
>>>Maybe some of these could find their way into FPGAs...
>>
>> Heh, they could at that. Though I've not yet read these 
>patents, I've been working on what I would > call "waveshaper 
>feedback synthesis" or perhaps "strange sine synthesis" where I 
>have used sine > oscillators with other than simple feedback to 
>produce more waveshapes than the almost-sawtooth. > > A while 
>back I did some experiments with trig identities to "morph" 
>between sin(wt) and sin(2wt) > and a couple of others. I dropped 
>it because it was mainly underwhelming. Perhaps these patents > 
>will show me things with more whelm. > > -- ScottG 
>
>
>You mean like Chebyshev polynomials? 

Heh, no, just the basic trig identities, here's some C code which I used as the basis for the FPGA
design:

// parametrically controlled double angle formula
// P is the morphing parameter.
//  out = ( sin( angle ) * ( P * cos( angle ) + ( 1.0 - P ) ) ) * ( P + 1.0 )  ;
//
//   This code is from the doubler/tripler which morphs sin(3u) to sin(u)
//   double f0( double u, double P )
//   {
//   double n;
//   n = ( sin( u ) *  ( P * cos( u ) + ( 1.0 - P ) ) ) * ( P + 1.0 )  ;
//   return( n );
//   }
//
//   double f1a( double u, double P )
//   {
//   double n;
//   n = ( f0( u, P ) * ( P * cos( u ) + ( 1.0 - P ) ) - (P/2.0)*sin( u ) ) * ( P + 0.90005 )  ;
//   return (n);
//   }

I have the wikipedia page open for Chebyshev polynomials so I will read that over and see what I see.

>I didn't think they were so 
>interesting either until I learned that they could be added 
>together for combined results.  Of course you can still only 
>properly input a fixed amplitude sine wave, but you can get an 
>arbitrary harmonic series out.  Of course this isn't a huge 
>revelation since you can do the same by using a waveform other 
>than sine and skipping the polynomial waveshaper business... 

Thanks Scott, I will have to look into this more deeply.

-- ScottG
________________________________________________________________________
-- Scott Gravenhorst
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