Most of you are partly right.
The problem is that mostly no signal is broadcast at 1080i x 1920 since most of the programming is dumbed down in the recording distribution format of HDCAM to horizontal 1440, not 1920 unless it was done using the latest HDCAM equipment which does offer enhanced hor resolution. There are some that may offer the full ATSC Horizontal spec since the video was studio produced and recorded with equipment capable of this higher standard. The reality is there is far more equipment in use today that is HDCAM standard. e.g. HDNET uses older cameras that are 1080i x 1440. There is no putting back extra digital information when it wasn't captured in the first place. But on top of this production standard, the fact is that all network programming regardless of whether it was shot with new or older cameras, or even on film, is all CONVERTED to a single limit standard as a matter of network or station policy. They have to do this for technical reasons to prevent the transmitter from going nuts everytime a different bandwidth enters the TV production.
But the real answer to the dilemma between 1080i and 720p is that 1080i is indeed an interlaced format that was invented to first offer the highest quality signal and remain within the original 6Mhz channel spectrum
and be properly displayed on a CRT analog monitor. 720P x 1280 was an equivalent set of standards to produce a progressive frame image that
is better displayed on a digital pixel based monitor and still offer the highest image for that monitor type. Conversions of 1080i to progressive for the purpose of display on a digital monitor will indeed reduce the line base to 540 V pixels as the odd and even scan lines are combined to meet the frame rate. 1080i is 60 fields per second. But the complete 1080 screen frame takes full two fields to make and that is still 30 FramesPS ( note these are color corrected for timing in NTSC / ATSC to 29.97 fps for sync match on the real time clock but we don't need to get into that here as it relates to another complication of the exact timing of video. If you wanrt to know that, it is a topic for a different thread.)
So the end of the story here is that in effect, when viewed on their own high end
intended display system both will have about equal image quality with respect to vertical and horizontal detail. Unfortunately, the 1080i x 1920 requires an extremely expensive monitor system to display that resolution as it was designed. Today most people have switched to digital displays that are pixel based and progressive ( progressive means that the image gets flicked on in an instant on the screen rather than being painted left to right, top to bottom twice (interlaced) over a length of time. The image remains on screen as it is painted like this due to a chemical property of the screen called phosphor persistence). But TV Networks still transmit with interlace so you need to do a conversion and whether you do that in the receiver or the monitor is the real question. Regardless of where you do the conversion to progressive it is a given that Progressive is ultimately where you will end up in the signal just before you see it as light on your screen.
Now enter the latest 1080p60 x 1920. This is a newer format that represents the highest current TV standard offered only in Blue Ray and some camcorders. No tape format currently offers this level of bandwidth we can buy. Blu Ray disk is your best option to see this. It will offer the highest quality video and can only be displayed on an appropriate digital monitor.
So what about 24P. The main purpose of 24P is to achieve the high resolution quality of BluRay format ( 1080p x 1920 but reduce the frame rate to 24 frames per second to match celluloid film which is always at 24 FPS for presentation. BY not converting the original program film from 24 fps to 60 fps ( 59.94) certain conversion artifacts are eliminated and you see the film in not only the highest resolution but also the least amount of conversion artifacts because there is no conversion from film to your display.
So what are the conversion artifacts that you get when watching a 24 fps film at 60 progressive video frames? Ever notice the right to left pan blurriness in a film on Blu Ray? If you don't ever see tyhis it is likely you are viewing at 24 P. If you do see this you are viewing at either 30 p or 60 p on your monitor. contrary to what some believe, there is no gain to resolution with 24p, only eliminate motion artifacts.
So the end story on best quality today is this-
Best Blue Ray Video is at 1080p60 x 1920
Best Blue Ray from films is at 1080p24 x 1920
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Most 1080p24 monitors will have an automatic switch when connected by HDMI to a BluRay player. The PPV 1080p24 movies that Dish is doing work much in the same way by testing your connection and if allowed, you'll will see the movie film at 1080p24. If not it comes in at the Video rate. ( I'm not sure if they do p30 or p60 as the only one I have watched was a film and it was appropriately seen here at p24.)