Am 22.09.2016 um 12:18 schrieb André Michelle:


How do I detect discontinuities? It is easy to see when printed visually but I do not see how I can approach this with code. Do I need the ‘complete’ function at once and check or can I do it in runtime for each sample. I think so since you suggest that I can jump around within the function without alias? Because that would sound like a solution I wanted to have from the very beginning.

You "detect" them they way you construct them.
For instance you have a phase ramp, say from -.5 to .5, you know that the discontinuity happens when your phase + frequency_step is > 0.5, and it happens in that fraction of a sample when the phase would be 0.5, so it happens at (phase + frequency_step - 0.5)/frequency_step fraction


I do not quite get this: C(1). Does it mean I have C(n) values of the function where C(1) is the second value?

It's about differentiability and smoothness
"The function f is said to be of differentiability class Ck if the derivatives f′, f′′, ..., f(k) exist and are continuous"
See https://en.wikipedia.org/wiki/Smoothness
But you can ignore this for now...


What frequency does the integrated sync function has?

It has the same bandlimit as your waveform should have

What is a 'fraction of a sample'?
The jump in your sawtooth waveform happens within a fraction of a sample time, as explained above When you read your wavetables you also read them at fractions of a sample (and interpolate to get the value at this fraction of a sample), all your signal exists also between samples.


I am missing to many aspects of your suggestion. Any hints where to learn about this would be appreciated.

I also have a question: what is the benefit of having a synthesizer in a webbrowser?

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