# Simulating musical instruments using their impulse response

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

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.