[sdiy] Fourier Analysis Question

[Tom Wiltshire]

Paul,

On 17 Dec 2010, at 15:52, Paul Cunningham wrote:

> word. Im interested in this sort of thing being an owner of the kurzweil 150 (fs) and absolutely *love* the dynamics of their FFT based piano. unfortunately it is bandwidth limited to 10k. so i guess one consideration is the necessary output sample rate. the other i guess is how critical the individual sine phases are over time, since you will be interpolating (like a waldorf does).
> 
> how many wavetable slots are necessary to get an accurate sound? you will need more different waves for the attack, but i suppose the partial phases become a lot more important for the sustained portion since pianos have up to three strings per note and your wavetable would need to represent that movement by scanning a loop or being really long. would you try to modulate the wavetable scanning or just run from front to back at a linear rate? what are your thoughts on that? -pc

I suppose there are two approaches: Place the waveforms irregularly in the wavetable and then scan it all linearly, or change the rate at which you interpolate between different waveforms. To my way of thinking about it, the second is easier, but waldorf did it the first way, since they didn't have the options we have now.
The partial phases is a very good point. Usually you'd want to keep phases the same for wavetable interpolations, since that way you get a linear variation in harmonic amount from one wave to the next (e.g. it is a strictly linear mix). If you change the phases, the change of harmonic amount is not likely to be linear. If I can get to a series of waveforms, I could ignore the phase and see if what comes out remains "pianoey". It'll no longer match the original waveform, but would keep the same harmonic content and approximately similar harmonic evolution. Will it still *sound* the same as the original? That'll be an interesting experiment. Anyone got any experience of wavetable synthesis with waveforms with varying phases to offer?

Tom