Ah, but then it becomes a COMPLETELY different problem :-)
First: Congratulations on buying a SPLENDID TV :-)
Secondly: The Amiga will not generate 1080i or 525p/480p. The standard Amiga graphics chipset is capable of delivering 525i and 625i (normal NTSC/PAL resolutions) plus 625p and 525p/480p (AGA). But only in composite/RGB. A graphics card is needed to produce anything in 1080i (ok, it CAN create something in that ball park, but the speed will be CRAP and the horisontal resolution will still be 640, NOT pretty ;-) ).
A Voodoo3 or other gfx cards using P96 can easily be set up to produce ANY resolution you want, including ALL the known HDTV resolutions. You just need to convert the RGBHV output to YPrPb.
Best device I have found so far seems to be:
http://www.ramelectronics.net/html/kd-vtca2.htmThis will do excactly what you want. The PC software it comes with is almost as good as PicassoMode that comes with P96 on the Amiga.
But again, you need a graphics card to have much benefit from this. Allthough a quick phone to those people to check that it can indeed take the resolutions an AGA Amiga generates (make a list containing PAL, NTSC, Multiscan and Productive with all frequencies and all other data from the AGA manual addendum) might be helpful.
Good luck, and tell me if you buy one. I am thinking of doing it myself.
Edit:
God damn, ATI make a box for 1/7 the price of the above that claims to do the same.
USD29 or so seems to be the price. Check that as well. Still need VGA to make good high-res signal, but pal/ntsc/multiscan should at least work. I am _really_ confident in that ;-)