band limited oscillators

[Tom Adam]

And here's the link:
http://search.retrosynth.com/synth-diy/


On Feb 6, 2009 13:08 "Tom Adam" <tom.adam at thebigear.be> wrote:
> It is a cool list. Lately there were indeed a lot of SW related
> topics.
> If you want SW topics only, there are better list I guess.
> I would say it's like 85% HW, rest is SW related.
> There is an archive somewhere, but I don't have the link here. You
> could check this to see if it's your cup of tea.
> 
> Cheers,
> ToAd  
> 
> 
> On Feb 6, 2009 12:57 "M-.-n" <nostromo at arkaos.net> wrote:
> > Thanks Chris, that’s a really interesting executive summary !
> >  
> > How’s the list, I always thought it was mainly hw based but it
> > seems
> > there’s some software one too… what’s the ratio between the two ?
> > Should
> > I join ?
> >  
> > M.
> >  
> > From:music-bar-bounces at lists.music-bar.org
> > [mailto:music-bar-bounces at lists.music-bar.org] On Behalf OfChris
> > Strellis
> > Sent: vendredi 6 février 2009 9:25
> > To: Music-bar
> > Subject: RE: band limited oscillators
> >  
> > I can offer some tips sent into the SDIY list recently from the
> > great
> > Antti Huovilainen
> >  
> > <http://antti.smartelectronix.com/>
> >  
> > also <http://www.diy.synth.net/gallery/main.php?g2_itemId=1078> 
> > Synth
> > DIY UK 2006
> >  
> > Some DSP theory links here:
> > http://www.chameleon.synth.net/english/links.shtml
> >  
> > > 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
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