What is better 1080P or 1080i?

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1080p - the frame is produced by using a single progressive scan.

1080i - the frame is produced by using two simultaneous diagonal scans.

Human eye cannot differ the two resolutions, so paying an extra £1000+ for 1080p is definitely wasted money.

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I think that 1080p does give a better picture, but you can only start to appreciate it on the bigger sized tv. For a 1080p screen to be noticably better than a 1080i one, you would probably need a screen size of over 60".

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The human eye can actually tell the difference very well, especially when watching fast action or sports. 1080p is technically better to watch, but theoretically worse because it does not have the two sets of 540 interlaced lines being displayed alternately. Because each frame is composed of two separate lines being displayed and two moments in time, if the recorded object moves fast enough to be in different places when each field is captured it creates a 'combing' affect. So technically 1080p is better especially when you watch closely.
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It also depends on the output of the signal being sent into the HDTV. over 85% of tv networks are being broadcast into 1080i the rest is 720P. When will they switch to 1080P? They won't it took over fifty years for the government to change the standard and it hasn't even been effect yet. Stations have already committed to either one of the standards and will be unlikely to change anytime soon.  

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On an Interlaced Picture the scan lines of a frame are arranged in two fields each. One of the two fields contains the odd lines and the other field contains the even lines. Interlacing is when these two fields are shown in sequence at twice the rate of the actual frame and at half the resolution. So each half frame is shown and is slightly different.

In the UK PAL televisions operates at 25 frames a second with 50 fields a second (USA 30 frames a second with 60 fields a second). A broadcasted signal that is Interlaced requires half the signal bandwidth of a Progressive signal. A progressive signal has a scan rate of 50 full frames per second compared with an interlaced signal which has half the frame speed.

Interlaced pictures on recordings made for television or with a video camera aren't able to be displayed on standard definition LCD televisions and Plasma televisions. This is because the picture isn't created with an electron scan like CRT tv's so LCD televisions and Plama TVs don't gain from the interlaced picture signal. Flat panel widescreen televisions have internal processing to create a progressive scanned picture from a interlaced image - i.e. Deinterlacing.

Progressive scanning is a method to display, transmit, and store a moving picture. Each frame has all of the lines instead of even lines or odd lines as with an Interlaced signal and they are shown in sequence.

The benefits of Progressive Scanning is that there is a greater vertical resolution than on Interlaced pictures at the same frame rate with out blurring, interlace artifacts, and reduced eye strain. It is also possible to scale to a higher resolution than it is with comparable interlaced sources. Because interlaced signal sources have to be deinterlaced before scaling with obvious combing artifacts, Progressive scanned full images give the best results when scaling.

The conversion of a progressive source such as 1080p/50 into an interlaced configuration such as 1080i/25 is easier than the conversion of an interlaced signal to a progressive format.

On a still picture there wont be any difference in picture quality between 1080i and 1080P. However with a 1080P source on moving images the 1080P will produce more fluid motion and higher resolution

If you don't intend to use a Blueray player, PlayStation 3, or to download films from the internet then a HD ready 1080i/720p tv will probably suffice. However if you want to future proof your self against possibility of future Full HD 1080p broadcasts then the full HD 1080p models are the ones to buy. Obviously if you have or are going to buy a Blueray player, PlayStation 3 or to you are going to down load full HD films then the full HD 1080p is the logical choice.