Also, I am not totally sure sum of sines is equivalent to DSP filters. I mean, in a stationary state it IS equivalent, but when you modulate the cutoff the output signal is in a non stationary state and I don’t think the additive synthesis is then equivalent to the DSP.

I am sure I wrote that but I must have deleted it:

The polyBLEP method can really be seen as adding to a hard angle sawtooth the right residu to kill the hard angle and put a soft angle in its place. It’s also what filtering does but here it’s not really that. I mean that it’s an analytic method, so it can be formally/analytically computed for any frequency without storing anything. It’s just a 2 order polynomial added to the sawtooth.

Saw being the hard angle sawtooth, theta being its phase, and dTheta the frequency/sampleRate:

```
if theta < dTheta:
theta /= dTheta
saw-=theta+theta-theta*theta-1.0
elif theta > 1.0-dTheta:
theta=(theta-1.0)/dTheta
saw-=theta *theta +theta+theta+1.0
```

And you’re right about the x(t)*y(t) part. But it’s kind of an extreme case you took. Most of the time, this kind of multiplication happens between an osc and an lfo.

Personally, for my usage, I’d like to stay minimalistic so not complicate the code too much to take into account extreme/rare situations. My goal is to tweak the code creatively during the music composing process, so I need a base-code that is simple and tweakable.

I will focus on the numpy pre-buffering idea and the convolve method. Right now I am worried about the fact that I would need to compute the impulse response each time the filter parameters are changed...

If I use my 16 poles filter with a 10 order approx of each IIR one pole filter in it, it means I have to compute a 160 coefs impulse response everytime a parameter is changed. I wonder if it’s really manageable for fast filter sweeps. One solution might be to compute these 160 coefs for each value of the filter’s parameters, so a 160xN matrix if only cutoff, but a 160xNxM matrix if cutoff+resonance...

I’ll probably end up not using convolve because of that. But I am planning to add an additive synthesis functionality so that a special additive generator can emulate a sawtooth+filter. Even if it’s not mathematically equivalent when the cutoff is modulated, it’s probably musically interesting ;)