Krzysztof Czaja hat gesagt: // Krzysztof Czaja wrote:
finally found some time to look closer at the math (I am math-blind without a sheet of paper).
Me, too. And I should have used wrap~ indeed, that does the same [>~ 1] and substracting 1 or 0, I just didn't think of it. All those objects...
The min~ solution is apparently cheaper than Varga's, and the output scaling is not tricky at all -- it is: ((a + 1) / a) * min~(x, a *~ (1 -~ x)). The input (`a' coeff) scaling is best done with an exp, in order to have symmetric control around zero.
The important idea behind Varga's algorithm is "Bandlimiting". The standard phasor has harmonics beyond the Nyquist frequency because of the abrupt changes from 1->0 and unfortunatly now that I took a sheet of paper, the way I realised trisaw has the same problem. Duh. I looked closer at Varga's code and he uses a new Csound function table generator, GEN30. This does the following:
"GEN30 extracts a range of harmonic partials from an existing waveform"
The 4(x-x^2) expression is used in Varga's code to fill a table with such a waveform, that GEN30 then reads while limiting the upper border of the harmonics range.
Because these gen30-generated table later is used in an oscili (==tabosc~ in PD) with varying frequency, one cannot simply use one table for every trisaw~ frequency, because that would introduce aliased frequencies again. Varga's solution is to fill 128 tables, one for each midi note, with GEN30-functions from 4x(1-x) polynoms and limited upper harmonic borders of "nyquist_frequency/note_frequency"
All this I didn't do in my trisaw~ and so I alias the same amount as you.
Life's a dog.
ciao,
Frank Barknecht _ _______footils__