Question about SFX...

[HSPuppets]

I'm trying to put together a sprite that has a lot of SFX (the utsuho reiuji sprite) and almost all of its SFX have a black background to them. I'm not exactly sure how to work with that, since some of the sprites fade in to the background. Do I have to manually remove the black background and work from there? It'd be much appreciated if I could get some insight on this.
Thank you.