Hi Oleg,
That all looks good to me - cool new operator!
Ideas for xxx:
sidebands
trigexpand
trig_harmonics
We were really looking for this kind of thing back in the 70s!
Cheers,
- Julius
On Tue, Nov 14, 2023 at 10:53 AM Oleg Nesterov wrote:
> On 08/21, Oleg Nesterov wrote:
> >
> > On 08/20, Julius Smith wrote:
> > >
> > > Pretty fun! This looks closely related Andy Moorer's technique:
> > >
> > > @ARTICLE{MoorerDSF75,
> > > AUTHOR = "James A. Moorer",
> > > TITLE = "The Synthesis of Complex Audio Spectra by Means of
> > > Discrete Summation Formulae",
> > > JOURNAL = JAES,
> > > VOLUME = 24,
> > > PAGES = {717--727},
> > > MONTH = dec,
> > > NOTE = "Also available as CCRMA Report no.
> > > \htmladdnormallink{STAN-M-5}{
> https://ccrma.stanford.edu/STANM/stanms/stanm5/
> > > }",
> > > YEAR = 1975
> > > }
> >
> > Thanks! At first glance I don't think this is very closely related
> > but interesting.
>
> So yes, this is another thing, I'll try to make another PR, I already
> have the code. Let's finish this discussion first.
>
> > > I vote in favor of the addition provided its well documented in its
> > > comments -> MarkDown extraction.
>
> OK. Please see the (same) code with the docs below.
>
> Is the documentation good enough for PR?
>
> And of course, how should I name xxx and yyy ? ;)
>
> Oleg.
>
>
>
> //-`(os.)xxx`--
> // adds harmonics to quad oscillator.
> //
> // Usage
> //
> // ```
> //cos(x),sin(x) : xxx(vs) : _,_
> // ```
> //
> // Where:
> //
> // * `vs` : list of amplitudes
> //
> // Example test program
> //
> // ```
> //cos(x),sin(x) : xxx((10,20,30))
> // ```
> //
> // outputs
> //
> //10*cos(x) + 20*cos(2*x) + 30*cos(3*x),
> //10*sin(x) + 20*sin(2*x) + 30*sin(3*x);
> //
> // ```
> //process = os.quadosc(F) : xxx((10,20,30))
> // ```
> //
> // is (modulo floating point issues) the same as
> //
> //c = os.quadosc : _,!;
> //s = os.quadosc : !,_;
> //process =
> //10*c(F) + 20*c(2*F) + 30*c(F),
> //10*s(F) + 20*s(2*F) + 30*s(F);
> //
> // but much more efficient.
> //
> // Implementation Notes
> //
> // This is based on the trivial trigonometric identities:
> //
> //cos((n + 1) x) = 2 cos(x) cos(n x) - cos((n - 1) x)
> //sin((n + 1) x) = 2 cos(x) sin(n x) - sin((n - 1) x)
> //
> // note that the calculation of the cosine/sine parts do not depend
> // on each other, so if you only need the sine part you can do
> //
> //process = os.quadosc(F) : xxx(vs) : !,_;
> //
> // and compiler will discard the half of the calculations.
>
> //-
> xxx(vs, c0,s0)
> = c0*vn(0),s0*vn(0), 1,c0, 0,s0
> : seq(n, outputs(vs)-1, add(vn(n+1)))
> : _,_, !,!, !,!
> with {
> // ba.take(n+1, vs)
> vn(n) = vs : route(outputs(vs),1, n+1,1);
>
> add(vn, co,so, cn_2,cn_1, sn_2,sn_1) =
> co+cn*vn, so+sn*vn, cn_1,cn, sn_1,sn
> with {
> cn = 2*c0*cn_1 - cn_2;
> sn = 2*c0*sn_1 - sn_2;
> };
> };
>
>
> //-`(os.)yyy`--
> // creates the list of complex harmonics from quad oscillator.
> //
> // Similar to `xxx` but doesn't sum the harmonics, so it is more
> // generic but less convenient for immediate usage.
> //
> // Usage
> //
> // ```
> //cos(x),sin(x) : yyy(N) : si.bus(2*N)
> // ```
> //
> // Where:
> //
> // * `N` : number of harmonics, compile time constant > 1
> //
> // Example test program
> //
> // ```
> //cos(x),sin(x) : yyy(3)
> // ```
> //
> // outputs
> //
> //cos(x),sin(x), cos(2*x),sin(2*x), cos(3*x),sin(3*x);
> //
> // ```
> //process = os.quadosc(F) : yyy(3)
> // ```
> //
> // is (modulo floating point issues) the same as
> //
> //process = os.quadosc(F), os.quadosc(2*F), os.quadosc(3*F);
> //
> // but much more efficient.
>
> //-
> yyy(N, c0,s0)
> = c0,s0, 1,c0, 0,s0
> : seq(n, N-1, si.bus(2*(n+1)), add)
> : si.bus(2*N), !,!, !,!
> with {
> add(cn_2,cn_1, sn_2,sn_1) =
> cn,sn, cn_1,cn, sn_1,sn
> with {
> cn = 2*c0*cn_1 - cn_2;
> sn = 2*c0*sn_1 - sn_2;
> };
> };
>
>
--
"Anything that can be automated should optionally be"
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