Hallo, Roman Haefeli hat gesagt: // Roman Haefeli wrote:
hey frank
oh! this is great! i don't have time right now to dig into it, but i sure will after the semester is over (in a few days). i was always looking for a way to create pwm (or other changeable bandlimited waveforms).
On Sun, 2007-12-02 at 15:19 +0100, Frank Barknecht wrote:
This approach has one big advantage over bandlimiting with pre-calculated wavetables as realized in some old patches by Guenther Geiger and newer ones by Roman: The waveforms can be changed on the fly, for example to do PWM on a rectangle wave, which is hard or impossible with pre-calculated bandlimited waveforms
yeah, i am looking forward to see an implementation of bandlimited pwm square (or making my hands dirty by trying it myself).
It's in the help-file, see the subpatch "even.odd". Or try attached variation.
i once read the chapter in millers book and also had a look at the example, but i haven't understood it. i hope your patches will help me understand better.
Well, the idea of transition splicing is quite simple: Every time you have a jump in a waveform, you replace that jump with the jump of a bandlimited square wave, scaled so the endpoints of the square and your original signal match.
If you do this for a [phasor~], you can construct all other waveforms with jumps, especially of course square/rectangle waves, but also more complex jump-waves using the technique of J02.trapezoids.pd (put [splicetrans~] after the [wrap~] there and connect the frequency inlets of it as well to try. I haven't yet managed to apply this technique for corners like in a triangle wave, but foldover isn't that bad there anyway.)
The square wave jump is constructed to be heavily bandlimited: It only consists of the first two or three square wave harmonics (1 and 3 and 5 times the fundamental). So whereas normally a jump will generate a lot of loud alias harmonics, using spliced transitions you can be sure to only get harmonics at the jump that are up to 3 rsp. 5 times the fundamental frequency. Then you're fine up to a fundamental of Nyquist/3 or Nyquist/5 - which would be 8000 rsp. 4800 Hz @ 48 kHz SR. This is already quite high for an oscillator: For 3951 Hz the midi note number is 107!
The tricky part is to actually patch the transition in Pd, but thankfully Miller already did it. ;) And now it's an easy to use abstraction as well.
Ciao
Frank Barknecht _ ______footils.org__