You have the same exact problem we had & Rowdy's method works. At least, it did for us. GSD Rescue people said Ziva was "good with cats". That was an important factor for us, as we have 4 housecats. And 1 of those was born crippled (Oliver) & I did NOT want anything to happen to him. Well, the rescue people must've beern looking at another dog, cause Ziva went postal every time she saw a cat. Her crate would bounce & she'd kick the tray out about 6". Snarled, barked, growled.
We tried all the normal commands, nothing worked. One night, I held Oliver on my lap while hubby approached with the dog. She's allowed to sniff, that's all. Lots of praise. (We'd stopped the treat frenzy by that time). It's been about 8 months now - Ziva stays in the living room, outside her crate. The cats enter by way of walking thru their cat tree - they all prefer her water bowl to their own (yuck - don't know why, with all the gooble-de-gook that lands in the bowl when the dog drinks...) She does not close her eyes --- watches them ever-so-closely.
Wanna borrow my Sam? (8 yrs old, big black cat, declawed fronts) He gave the dog a couple of lessons & that's all she needed to put her over the top. He decided he wasn't going to back down any more, sat on his haunches, & boxed her muzzle.
She'll still chase, if she can, but at least now we can stop it. And she walks wwaaayyy around Oliver & Sam now.