Make a few short sinew backed bows first. Asiatic composites are the most complicated bows to build, you need to cover a few bases first, or you will regret it.
I'd like to build one one day as well, I'm starting on a couple North American style horn bows first, just horn and sinew, no wood core. Next I'll try a spliced lever bow with a sinew backing, than maybe I'll have the confidence to attempt an Asiatic style horn bow