Hmmm, here is the interesting part of user guide of my transmitter (Philips SWW1800) :

The 1080p support is very limited (no 50 Hz / 60 Hz). I suppose it is implied by the wireless bandwith.
Winston Churchill wrote:
In actual fact, I believe that your problem is that not only is your transmitter not fully compatible with the Apple TV, it is probably not fully compatible with your TV.
Hopefully my transmitter works very well with all my devices excepts ATV3 :-) PS3 is well supported with 1080i 60 Hz mode. Neufbox TV (kind of digital decoder) works well with 1080i 50 Hz mode.
Conclusion : I will not be able to see any HD 1080 movie with my Apple TV 3 as long as it doen't support any 1080i mode. Am I right ?