# [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
http://www.matteosistisette.com

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