Off Topic Productions

I don't know if anyone here will know the answer to this, but I have been trying to find an answer to this for a while, but can't find an exact answer.

I live in the UK and we use the PAL Television system and the content is broadcast at 625 total lines, 576 active lines, 25.00 frames/sec 50 fields for 50hz televisions. In the USA they use NTSC and the content is broadcast there at 525 total lines, 483 active lines, 29.97 frames/sec, 59.94 fields for 60hz televisions.

Does anyone know how television networks broadcast a TV show made for a different TV system and still have the show playback smoothly? Especially when the amount of interlacing lines and frame rate is different? Such as a UK, PAL TV Network broadcasting a TV Show made for American TV which is NTSC?

Morpheus wrote: Does anyone know how television networks broadcast a TV show made for a different TV system and still have the show playback smoothly? Especially when the amount of interlacing lines and frame rate is different? Such as a UK, PAL TV Network broadcasting a TV Show made for American TV which is NTSC?

It's very likely converted from one to the other. Any video editing software will do this if you set the output properly, so it shouldn't be a stretch that they convert whatever they have from one thing to the other.

It is probably filmed and mastered in another format anyway which gets converted.

Regarding the different framerates:

A possibly equivalent question you may ask is if I'm playing a game which is getting a steady 55fps but my monitor's refresh rate is 60Hz how does that work? What about if I'm getting 100fps. The answer to those questions is that every time your monitor goes to display a frame it will grab whatever frame the graphics card tells it. If the graphics card doesn't have a new frame ready it will just repeat the old one. As such your monitor will render at 60Hz but if you're only rendering 55fps then 5 of the frames your monitor renders will be exact repeats of the frames before them. Similarly if you're rendering 100fps, 60 of the frames will simply be thrown away. This assumes you have vsync enabled. If not, you could be part way through rendering a frame when the monitor grabs the data and as such you end up with the top half of your screen displaying one frame and the bottom half rendering the frame before it (or after it. I'm not sure).

I'm not sure if tv broadcasts do the same thing but if you've ever played a game at close to but not quite 60fps it mostly looks fine. So a broadcast of a 24fps signal at 29Hz could just duplicate 5 of the images. A 29fps signal at 24Hz could just throw away 5 of the images. In reality there are probably cleverer things one could do but they may not bother.

As for the difference in resolution. A fancy way of creating a big image from a small image or vice versa is to do a fourier analysis of the intensity of the pixels over the image. If you're creating a smaller image you then throw away all the high frequencies that cannot be represented on the smaller image then invert the fourier transform to generate a new function in image space. You can then sample that function to get the pixels for your small image. Going from small to big is the same but you don't need to cut the high frequencies. If memory serves there is a more clever way to decide pixel intensities from the image function but I don't recall how it works.

Whether they do this or not I don't know.

If you're not familiar with fourier analysis, the basic principle is that you can represent any function as a sum of sine functions with different frequencies and amplitudes. So say I have a function f(x) then I can approximate this function as f(x) = a + b.sin(x). This is not a very good approximation but I can make it better by saying f(x) = a + b.sin(x) + c.sin(2x). Better still f(x) = a + b.sin(x) + c.sin(2x) + d.sin(3x). I don't recall if the sequence 0,1,2,3 that I've used there is correct and I don't recall if you need cosines as well but that's the general idea. The approximation gets better and better the more terms you have. Fourier managed to prove that your approximation would continue to get better as you added more terms and, importantly, how to calculate what the values of a,b,c,d,etc are.

The idea of cutting out higher frequencies is that if you have fewer samples you aren't able to represent high frequency samples easily. By high frequency I mean the later terms where the number in front of the x is very large. This called something like the Nyquist limit and is the same reason the bandwidth is limited on an internet connection.

Effectively what this means is that if you have a a series of values y1,y2,y3,y4.....yn you could say that y1=f(1), y2 = f(2), yn = f(n). This defines f(x) at those values. Then you can convert this into the coefficients a,b,c...etc from above. An interesting sidenote is that if you have n values y1,y2....yn you can often recreate the function pretty well with less than n coefficients. This is the principle behind jpeg and mp3 compression (mp3 also has the luxury of being able to simply ignore all the frequencies that the human ear can't hear).

So our series of values y1,y2,y3...yn could be the intensity of all the pixels. As such we can use this to determine f(x), then use fourier analysis to determine a,b,d,...etc, maybe cut out some of those values because we don't need them, then revert the fourier analysis to get F(x). Then evaluate F(X) at 0,1,2 etc to get your new pixel values.

You might reasonably ask, if we already have f(x) what's the point of converting to frequency space and then right back again. The key is that you don't truly have f(x). In actuality you just have the values f(1), f(2), etc. F(X) you can evaluate at any value so you can take F(2.5) to determine what the pixel halfway between pixels 2 and 3 should look like.

DFTs are rather the standard way in DSP for resampling, not some fancy.
However, the same approach works for temporal domain too, so you can use that to resample the framerate. Or maybe even do this all at once with a 4D filter, but probably different windowing functions for temporal and spatial domain are used.

good point. You could just use the same solution in the time domain.

Been really busy with one thing or the other over the past few months, but thanks everyone.

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