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I studying DSP and trying to find the limitation of 'teaching' a software to emulate a musical instrument by sampling its notes at different velocities and building an LTI system for simulating it.

Is that feasible? is that even LTI? is that limited to certain instruments only? what are the problems I'm about to encounter trying to do that?

Thank you

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there are a lotta people doing research regarding music synthesis and DSP. yes you can sample notes and different key velocities and play them back with different MIDI velocity parameters. if you wanted to somehow interpolate between a note played at $mf$ to $f$ and on to $ff$ and $fff$urther, you would need to find a way to phase align the waveforms. IMO the only decent analytical way to do that in the time domain is wavetable synthesis where the wavetables can be lined up (or it's frequency domain, it's called additive synthesis) - additive synthesis is more general, wavetable requires the overtones of the note to be mostly harmonic. doing this stuff right is not particularly easy.

on the other hand, since you brought up "impulse response", there are folks who do physical modeling of musical instruments, where they model the instrument as a form of resonant LTI filter and they separate the impulse response of the LTI filter from the driving function, which is not an impulse but something more. then, for different key velocity hits, they have different driving functions but the same LTI impulse response. sometimes it's called commutated synthesis or https://ccrma.stanford.edu/~jos/pdf/svd95.pdf.

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