[PD] Band-limited waves was Re: Max Smoother Audio than Pd?

Matteo Sisti Sette matteosistisette at gmail.com
Sun Mar 28 16:47:55 CEST 2010

 > Well, that is only if all the partials remain under the Nyquist
 > frequency. The idea is to limit the higher harmonics to the ones
 > described by whatever formula you use to generate the waveforms,
 > but if you eliminated all of them them you would just have a sine
 > wave again ;-)  So what you get is considerably less aliasing,
 > but without
 > oversampling and filtering you will still get some.

Please correct me if I am wrong:

You can choose between allowing for just a little bit of aliasing, or 
loosing just few highest harmonics...
("a little bit" and "few" may become "a lot of" if the span of pitches 
you are going to synthesize with one single wavetable grows)

The idea is:

1) Determine the amplitudes and phase of all (infinite) theorically 
needed harmonics (by fourier analysis of the waveform, not digitally in 
the patch but with paper, equations and books)

2) Generate a wavetable which is a sum of sinusoids with the amplitudes 
and phases determined at setp (1), but discard those that exceed the 
Nyquist frequency (index>=N)

Now, the index N of the first harmonic to eliminate depends on the 
frequency at which the wavetable is going to be reproduced,
And you obviously cannot (usually) generate as many wavetable as the 
pitches to be played which may be infinite.

So you may for example generate one wavetable per octave, or per 
whatever interval: then you have to choose whether you take all the 
harmonics "needed" for the lowest end of the interval, thus getting a 
little bit of aliasing, maximum at the highest end of the interval. Or 
you take all the harmonics "needed" for the highest pitch in the 
interval, in which case you never have even the least amount of 
aliasing, but you get a wave that "misses" the highest harmonics when 
the wavetable is played at a pitch approaching the lowest end of the 
interval assigned to that table......

Is this correct?

Matteo Sisti Sette
matteosistisette at gmail.com

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