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<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>I can offer some tips sent into the SDIY list recently from the
great Antti Huovilainen<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><a href="http://antti.smartelectronix.com/">http://antti.smartelectronix.com/</a><o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>also <a
href="http://www.diy.synth.net/gallery/main.php?g2_itemId=1078">http://www.diy.synth.net/gallery/main.php?g2_itemId=1078</a>
Synth DIY UK 2006<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Some DSP theory links here: http://www.chameleon.synth.net/english/links.shtml<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoPlainText>> I'm curious, what approach are you using to get
'alias free' oscillators? <o:p></o:p></p>
<p class=MsoPlainText>> Simply using a much higher internal sampling rate
and then a low pass <o:p></o:p></p>
<p class=MsoPlainText>> FIR filter? Or something more sophisticated
than this.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>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.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>1) Trivial saw with oversampling<o:p></o:p></p>
<p class=MsoPlainText>Pros: Easy, can do any waveshape, allows simple sync and
FM<o:p></o:p></p>
<p class=MsoPlainText>Cons: Requires massive (64..256x) oversampling to sound
good<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>2) Sum of sines<o:p></o:p></p>
<p class=MsoPlainText>Sum nyquist/freq number of sines to produce exactly
bandlimited sawtooth.<o:p></o:p></p>
<p class=MsoPlainText>Pros: No aliasing<o:p></o:p></p>
<p class=MsoPlainText>Cons: Too slow to be of use in practise.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>3a) Differentiated parabole wave<o:p></o:p></p>
<p class=MsoPlainText>Synthesize parabole (diff(phase^2)*1/freq for -1 <=
phase < 1). Aliasing falls at 12dB/oct (compared to 6dB/oct for trivial
saw).<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>Pros: Almost as easy as trivial saw. 1/freq can be
derived from interpolated table lookup (store 1/freq for each note)<o:p></o:p></p>
<p class=MsoPlainText>Cons: diff(phase^2) can get very small for low
frequencies requiring 24 or<o:p></o:p></p>
<p class=MsoPlainText>32 bit resolution. Requires 1.5-2x oversampling to avoid
annoying warble between 10-20 kHz.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>3b) Slewrate limited saw<o:p></o:p></p>
<p class=MsoPlainText>Use a trivial saw-tri pwm oscillator with the pulse width
set to exactly one sample. Can be shown to be equivalent to 2a.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>Pros: Doesn't require frequency dependent scaling or high
resolution computations.<o:p></o:p></p>
<p class=MsoPlainText>Cons: Same as 3a<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>3c) Other waveshaping methods<o:p></o:p></p>
<p class=MsoPlainText>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.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>4) Mipmapped wavetables<o:p></o:p></p>
<p class=MsoPlainText>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.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>Pros: Good quality with higher order interpolator or
oversampling mipmaps. <o:p></o:p></p>
<p class=MsoPlainText>Can do arbitrary waveforms. Easy FM. Easy phase
distortion.<o:p></o:p></p>
<p class=MsoPlainText>Cons: Needs lots of memory. Number of harmonics limited
for low notes. <o:p></o:p></p>
<p class=MsoPlainText>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<o:p></o:p></p>
<p class=MsoPlainText>octave) to avoid missing frequencies between 15-20 kHz.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>5a) BandLimited Impulse Trains (BLIT)<o:p></o:p></p>
<p class=MsoPlainText>Synthesize bandlimited impulse train and integrate that
to produce saw.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>Pros: Good quality. No oversampling required.<o:p></o:p></p>
<p class=MsoPlainText>Cons: Complicated, slow, has numerical issues. Difficult
to do FM, PWM or sync.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>5b) BandLimited StEps (BLEP)<o:p></o:p></p>
<p class=MsoPlainText>For each oscillator reset, sum a bandlimited step with
the trivial saw. <o:p></o:p></p>
<p class=MsoPlainText>The steps are precalculated and stored in a table (can be
quite short when interpolation is used between two phases.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoPlainText>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.<o:p></o:p></p>
<p class=MsoPlainText>Cons: Requires a divide per cycle. Can be complicated:
calculating required table entry is not trivial when using sync or pwm.<o:p></o:p></p>
<p class=MsoPlainText><o:p> </o:p></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>HTH<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Chris<o:p></o:p></span></p>
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