of course, this is new to me, though all methods have been around for some time.
thanks to robin/rs-met i implemented some DSF (discrete summation formulas) which synthesize bandlimited waveforms in a single equation instead of calculating a bunch of partials. this includes band limited impulse trains (BLIT can mean this or b.l. interpolated tables, being my/a standard osc implementation).
essentially what this means is.. good for me, yay :p using doubles instead of floats means everything runs at twice the cpu load.. a DSF sawtooth is about 4x the cpu of an interpolated table. the benefit is that there is no aliasing (or, depending on algo, minimal), modulation options and they sound great.
in composition i only use synths i know the algo for so that i can improve it.. so thank god it means i can finally start using better oscillators in my composition
i ought to have a single osc synth out fairly soon - the alg is similar to a 1980's yamaha home keyboard i used to have - amazing tech innovation :O it sounds pretty good in 44.1k with doubles and uses some better filters.. i used the stilson/smith moog ladder filter and am impressed bcs i'm hearing tones out of it that sctually sound like moog synthesizers.
so - old news, but makes me happy, and fleshes out my palette a bit. of course, this doesn't bode well for sales until i find some way to expand these algorithms. i'm still using fairly naive methods of modifying these complex equations. and, it also means higher cpu use in my synths
as a developer who likes to increase public awareness, i'd like to share something i found on a mailing list.. it's nice to know what you're hearing. enjoy!
> > > I'm curious, what approach are you using to get 'alias free'
> > > oscillators?
> > > Simply using a much higher internal sampling rate and then a low
> > > pass
> > > FIR filter? Or something more sophisticated than this.
> >
> > Since this question gets asked a lot, I'll list some of the common
> > methods. Roughly from easy to hard. Oversampling here means proper
> > oversampling with high quality lowpass filtering before decimating
> > to
> > target samplerate. Simply averaging N samples will not work.
> >
> > 1) Trivial saw with oversampling
> > Pros: Easy, can do any waveshape, allows simple sync and FM
> > Cons: Requires massive (64..256x) oversampling to sound good
> >
> > 2) Sum of sines
> > Sum nyquist/freq number of sines to produce exactly bandlimited
> > sawtooth.
> > Pros: No aliasing
> > Cons: Too slow to be of use in practise.
> >
> > 3a) Differentiated parabole wave
> > Synthesize parabole (diff(phase^2)*1/freq for -1 <= phase < 1).
> > Aliasing
> > falls at 12dB/oct (compared to 6dB/oct for trivial saw).
> >
> > Pros: Almost as easy as trivial saw. 1/freq can be derived from
> > interpolated table lookup (store 1/freq for each note)
> > Cons: diff(phase^2) can get very small for low frequencies requiring
> > 24
> > or
> > 32 bit resolution. Requires 1.5-2x oversampling to avoid annoying
> > warble
> > between 10-20 kHz.
> >
> > 3b) Slewrate limited saw
> > Use a trivial saw-tri pwm oscillator with the pulse width set to
> > exactly
> > one sample. Can be shown to be equivalent to 2a.
> >
> > Pros: Doesn't require frequency dependent scaling or high
> > resolution
> > computations.
> > Cons: Same as 3a
> >
> > 3c) Other waveshaping methods
> > Several other methods can be used to sample a smooth function and
> > then
> > warp the spectrum to resemble saw. Generally slower and more
> > complicated
> > than 2a or 2b.
> >
> > 4) Mipmapped wavetables
> > Precalculate a version (mipmap) for each octave (or half octave)
> > with
> > exact number of harmonics. Select nearest mipmap and interpolate
> > the
> > stored waveform on playback.
> >
> > Pros: Good quality with higher order interpolator or oversampling
> > mipmaps.
> > Can do arbitrary waveforms. Easy FM. Easy phase distortion.
> > Cons: Needs lots of memory. Number of harmonics limited for low
> > notes.
> > Requires oversampling the mipmaps (using longer table than strictly
> > required by the number of stored harmonics) or using high order
> > (FIR)
> > interpolator. Requires oversampling or more mipmaps (half or
> > quarter
> > octave) to avoid missing frequencies between 15-20 kHz.
> >
> > 5a) BandLimited Impulse Trains (BLIT)
> > Synthesize bandlimited impulse train and integrate that to produce
> > saw.
> >
> > Pros: Good quality. No oversampling required.
> > Cons: Complicated, slow, has numerical issues. Difficult to do FM,
> > PWM
> > or sync.
> >
> > 5b) BandLimited StEps (BLEP)
> > For each oscillator reset, sum a bandlimited step with the trivial
> > saw.
> > The steps are precalculated and stored in a table (can be quite
> > short
> > when interpolation is used between two phases.
> >
> > Pros: Very good quality. No oversampling required. Can do
> > bandlimited
> > FM, PWM and sync. Probably the only method that can do audio rate
> > PWM
> > and sync.
> > Cons: Requires a divide per cycle. Can be complicated: calculating
> > required table entry is not trivial when using sync or pwm.
> >
> > HTH
> >
> > Chris
with my modest (ha) abilities, i can attest that this is a description of common methods, and not exhaustive, eg. one of the phase mod options in hyperion is bandlimited using a very crude technique (which is mostly but not entirely effective). everything sounds different.. and people use their own strength in implementation, parameter ranging et al.. so ultimately, the message here is that my plugs should be sounding a little different in the future
it's best to just find some code you can actually understand enough to implement that one.
don't blink if you see it for that price.