Shortest pulse width to support

[Z1202]

The reason would be that the BLEP series simply doesn't converge Not unlike Fourier transform, which doesn't have to converge for arbitrary analytic function (even if you take Cesaro convergence into account).

Actually, upon further thought you might be right.

The nth derivative of exp(a*t) comes out as a^n*exp(a*t), which tends towards zero for increasing n iff |a|<1, for all a in C (with a=0 giving us the constant function and a=i*b giving sinusoids). I'm not sure what to make out of this exactly (ie. what is the scale of "t"), except as far as it suggests there might be a dependency on the angular frequency.

Yes, the same happens, obviously, for the sine (which I guess must be corresponding to the fact that at w>pi the sine is no longer bandlimited). I was asking myself the same question regarding the time scale. My assumption is that the decay rate of the unit BLEPs themselves (as n grows) will depend on the time scale, so that the final convergence is time-scale-independent (as it should be). But I haven't verified that.

[mystran]

Btw, there might be some relevant information to be extracted from the literature of https://en.wikipedia.org/wiki/Prolate_s ... e_function which are eigenfunctions of the truncate+band-limited operation, which is more or less what we are usually trying to construct out of BLEPs.

[Kraku]

Reading this thread I can't help but think that it would be interesting to see one of you guys writing The Art of VA Oscillator Design

Would be educating reading.