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;
};
};
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