I have just broken out my Amiga 500 and Amiga 1200 after like 15 years. I have booted up and got an image on my Flat Screen LG.
My Falcon and Atari 1040Ste have also been resurrected. Now the big question I recall the Amiga had composite tv out.
I could not get a image with any of my Ataris. I connect the Tv port of Atari and audio out to composite in and audio in on the Tv. So I have a yellow red and white cable from the Atari to yellow red and white in on the flat screen tv.
In the mists of time i recall the tv out on the Atari needed a composite like plug on one end and rf connection that pluged in to the rf in on the tv. So one needs a cable like used in the Atari 2600 or Commodore 64 to connect to rf connection of the tv.
I can't find a 1040 Ste manual. The Falcon manual talks about tv connection, though though the actual cable is not names.