well it could be alot of different things like inlet airleaks, coils, leads, dirty carbys, electrical.
i would start with the simple things first an ill go out on a limb here as this happend to my brothers gsxr600 and sounded very much the same, well with his when you would accelerate hard it would cough fart and miss then cut out,and it did give a huge backfire when it cut back in aswell, it would even do it when going over a few hard bumps.
we then realised that when it cut out if we gave the side stand a kick / wiggle it would come back to life, the reason it was doing this is because under hard acceleration the bike would squat and the side stand would foul on the fairing enough to move it, due to this the side stand switch would release and kill the motor (saftey thing) then as you roll down the road it giggles itself back to place.
this is easy to test just use a cable tie to hold the switch in then take it for a spin, if it doesnt do it again its that.
if it is that you can leave cable tie on, fix it where its fouling or bypass the switch.
it may or may not be this but it is a simple test and if it is the problem your cheerin but if it isn't you only wasted 5 min of your life.
good luck mate
