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1080i was not created as a low bandwidth broadcast standard. That is a common misconception. It is a standard made purely for CRT display technology, which back in '96 was pretty much the only consumer display technology on the market.

Unlike flat screens / pixel based display technologies, the bottleneck in CRT displays is not the number of pixels in the front of the glass tube, but rather the speed and accuracy of the electron beam that lights up these pixels. Higher resolutions = higher electron beam speeds = more expensive tubes.

To get around this limitation consumer CRT TV's draw each frame in two passes. First the electron beam draws every odd horizontal line (the even lines in between remain unlit/black), then it makes a second pass filling in the missing even horizontal lines. This is called interlacing, and this is why all older video standards (VHS, LaserDisc, SD broadcast signals, 1080i HD signals) are interlaced. They were designed for CRT displays.

The HD-Ready standard on the other hand, is designed purely for modern flat screen technology where interlacing is pointless. If you run into bandwidth problems, then it's a better solution to transmit 30 progressive frames per second, rather than 60 interlaced frames. To recieve HD-Ready certification, a TV must be able to display 720 progressive horizontal lines (or better) at 60 frames per second. Since 1080i CRT's are technically limited to 540 progressive horizontal lines at 60 frames per second, they don't qualify for HD-Ready certification despite offering a higher effective resolution per second than 720p displays.

The downside to interlacing, and why progressive is considered better, is mainly line shimmer. Because of the lightning fast response times of CRT, and the fact that the electron beam can only light up one pixel at a time, an ugly shimmering effect can be seen on very thin horizontal lines. This makes a Windows desktop unwatchable on a 1080i CRT. However with games and movies visible shimmer is extremely rare, and HD CRT's are generally still considered to be superior to flat screens as far as movie/game image quality goes.

Another problem with interlacing is that the frame rate is limited to 30 frames per second. This is not a problem with movies, as they are shot at 24 frames per second, but many games render at 60 frames per second. On a 1080i CRT these games will display odd lines from one frame, then fill in even lines from the next frame. This leads to motion artefacts. Typically there will be jagged edges on diagonal lines during motion. However this is a minor problem as in my experience most people will not be able to spot this even if you point it out to them. Motion artefacts on flat screens because of low response times is generally considered to be a bigger problem.