By Chris Pirazzi. Thanks to Charles Poynton and Andy Walls for some insights on standard def square luma sampling frequencies.
Lurker's Guide Trivia Contest! If you know a way to derive the 12 3/11 MHz and 14.75 MHz industry-standard luma sampling rates, or you know some historical clues as to where they came from, then please send me some mail! The prize is your name in lights on the top of this page. Well, ok, your name on the top of this page. And maybe some other pages too!On this page you can find a set of points and ideas from various sources that may one day help us reach a final conclusion on the origin of 12 3/11 MHz and 14.75 MHz.
|From cpirazzi Fri Jan 17 14:55:21 1997 |From: cpirazzi@cp (Chris Pirazzi) |Date: Fri, 17 Jan 1997 14:55:21 -0800 |To: email@example.com |Subject: square pixel sampling frequencies | |Hi, | |I'm on a quest to find the "deep, dark truth" behind the square pixel |sampling frequencies used for sampling 525/59.94 and 625/50 video. | |In your book you mention "No SMPTE standard addresses square pixel |sampling of 525/59.94 [60M] video. I recommend using a sampling rate |of 780FH, that is, 12 3/11 MHz...." (p.216). | |I too have seen hardware use 12 3/11 MHz. Can you show me how this |number is derived? Can it be derived from values in specifications? | |Your book does not have a comparable suggestion for 625/50 video, |but the devices I've seen use 14.75 million pixels per second. | |Same question: Can you show me how this number is derived? Can it be |derived from values in specifications? | |-- | |In theory, we should be able to derive the 525/59.94 [60M] number from |ANSI/SMPTE 170M: | |1. Section 3.3: "The aspect ratio of the active picture area | shall be four units horizontally to three units vertically" | |2. Section 11.1: "fsc = 5 Mhz * 63/88" (subcarrier frequency) | |3. Section 11.2: "fh = 2/455 * fsc" (line frequency) | |4. from #2 and #3, derive line period LP as 572/9 us exactly | |5. guess at this definition for "active picture area" from #1: | | vertically: Figure 7: The active lines: | F1: 243 lines from line 21 to line 263 inclusive | F2: 243 lines from line 283 to line 525 inclusive | So the picture consists of 486 lines. | | horizontally: Figure 7 and Table 2: The active line period ALP | The period from "Blanking End" to "Blanking Start," or: | ALP = (LP-(1.5 + 9.20)) us = 4757/90 us | |6. since the picture has 486 lines vertically and its active region | has a 4:3 aspect ratio, then there should be 486*(4/3) = 648 samples | within the horizontal active region. | |7. so since the horizontal active region has 648 samples and lasts | ALP us, then there must be 648/ALP samples per us, which is: | | 648 / (4757/90) = 58320 / 4757 Mhz = 12 1236/4757 MHz | |which is not equal to 12 3/11 Mhz. | |obviously the weakness of this derivation is step #5: ANSI/SMPTE 170M |is fuzzy about _what_ region of the signal has a 4:3 aspect ratio! | |where does 3/11 come from ?! ---------------------------------------------------------------------- |From Poynton@Poynton.com Sat Jan 18 10:50:52 1997 | |> I'm on a quest to find the "deep, dark truth" behind the square pixel |> sampling frequencies used for sampling 525/59.94 [60M] |> and 625/50 video. | ... | |Get a copy of a SMPTE RP , "Picture centering and aspect ratio" ... ... | |> 5. guess at this definition for "active picture area" from #1: ... | | This guessing is what the new RP is supposed to address, but its numbers= | preclude an exact integer relationship. 12 3/11 MHz is very close; I can't= | remember whether 779 or 781 is closer to the RP's nominal, but 780 fh is= | sensible - divisible by 4, even! - so I recommend it.=20 ---------------------------------------------------------------------- (further nagging Charles) |From: cpirazzi@cp (Chris Pirazzi) |- | |now we've both read SMPTE RP 187 and we've seen that it specifies yet |another 525/59.94 [60M], 4:3 aspect, 2:1 interlace pixel aspect ratio, |160/177. this implies a square-pixel horizontal sampling frequency of | | 13.5 MHz * (160/177) = 4320 / 354 = 12 12/59 MHz | |and it implies | | (12 12/59 MHz) * (572 / 9 us) = 2471040 / 3186 = 775 35/59 | |square pixels per total line. | |-- | |the industry, however, seems to be using a horizontal sampling frequency |of 12 3/11 MHz, which implies: | | (12 3/11 MHz) / (13.5 MHz) = 10/11 (x/y) | |pixel aspect ratio, and which implies: | | (12 3/11 MHz) * (572 / 9 us) = 77220 / 99 = 780 | |square pixels per total line. | |-- | |[it seems that the RP will be ignored] and will serve only to confuse matters | |and what's worse, I still don't know the answer to my original question :) |which was: | |Q1: where does 12 3/11 MHz come from ?! | |- clearly, RP 187 cannot be used to derive it. | |- possibly, one may be able to derive it with a suitable definition of | "active picture area" in step 5 above. | |- presumably, whoever chose 12 3/11 wanted some value that would yeild | an integral number of total samples per line. | |- probably, some hardware engineer at Phillips chose 12 3/11, as opposed | to some other value that would also yeild an integral number of total | samples per line, because it happened one day that the 12 3/11 MHz | crystal oscillator that he needed for his prototype board was a few | cents cheaper than the other possible oscillators. | |it's this last step which I have never gotten any solid data on. | |who was it who first chose 12 3/11 ? why did he/she choose that? | |-- | |SMPTE RP 187 introduces two new questions: | |Q2: where does the SMPTE RP's 160/177 come from? | |Q3: after going through all the effort to specify 160/177, why does RP |187 informative Annex A part A.4 suggest resampling 525/59.94 [60M] |square pixels to nonsquare using a ratio of 11:10? | |-- | |Then, we switch over to 625/50, 4:3 aspect, 2:1 interlace video. | | LP = (1000000 us/second) / ( (25 frames/second) * (625 lines/frame) ) | = 64 us | |-- | |In this case, SMPTE RP 187 specifies a pixel aspect ratio of |1132/1035, which is just a little bit silly. This implies a |square-pixel horizontal sampling frequency of: | | 13.5 MHz * (1132/1035) = 30564 / 2070 = 14 88/115 MHz | |and it implies | | (14 88/115 MHz) * (64 us) = 108672 / 115 = 944 112/115 | |square pixels per active line. | |-- | |Instead, the industry seems to be using a horizontal square sampling |frequency of 14.75 MHz, which implies: | | (14.75 MHz) / (13.5 MHz) = 59/54 (x/y) | |pixel aspect ratio, and which implies: | | (14.75 MHz) * (64 us) = 3776 / 4 = 944 | |square pixels per total line. | |-- | |We are left with the same questions as 525: | |Q4: where does the industry 14.75 MHz come from? | |Q5: where does the SMPTE RP's 1132/1035 come from? | | - Chris PirazziFrom this thread, we can at least conclude that the industry-standard ratios were designed to yield an integral number of luma sampling instants per line. But as to where they actually came from: who knows?
Andy wishes to emphasize that almost all of the following is pure speculation and train-of-thought. But there seem to be some helpful new observations in here:
|Q1: where does 12 3/11 MHz come from ?! | |- presumably, whoever chose 12 3/11 wanted some value that would yeild | an integral number of total samples per line. Well, yeah. The idea was probably to keep the sampling frequency phase locked or aligned with the line frequency as that makes life easy. The result is, as you note, an integral number of samples per line. See below. |- probably, some hardware engineer at Phillips chose 12 3/11, as opposed | to some other value that would also yeild an integral number of total | samples per line, because it happened one day that the 12 3/11 MHz | crystal oscillator that he needed for his prototype board was a few | cents cheaper than the other possible oscillators. This is very unlikely. 12 3/11 MHz looks very deliberate, especially when one observes that 12 3/11 = 1080/88 and figures out its connection to the FCC's 63/88 * 5 MHz chroma subcarrier specification. See below. |it's this last step which I have never gotten any solid data on. | |who was it who first chose 12 3/11 ? I have no clue. I couldn't even find a copy of a standard that documents it. Although one 'net source says SMPTE 244M does. | why did he/she choose that? That part I think I have mostly figured out. Here are design constraints that I backed out of the number based on properties I observed and some research of some old IRE Proceedings. To summarize, I think the design criteria were something like these: 1. The sampling frequency should be such that it is phase aligned/locked with the NTSC line frequency of Fh = 4.5 MHz/286 ~= 15.73426 kHz 2. The sampling frequency should be such that the number of luma samples for the active part of a NTSC line (52.65556 us out of 1/Fh = 63.5556 us) is as close as possible to 640 samples without going below 640 samples. 3. The sampling frequency should be such that it is a small integer multiple of a frequency that no lower than the chroma subcarrier frequency fc = Fh * 455/2 = 63/88 * 5 MHz = 3.579 MHz that encompasses most of the luma signal bandwidth. 4. The sampling frequency should be such that it is simply related to the chroma subcarrier and line frequency, and perhaps maintains the properties used for selection of the original chroma subcarrier (closer analysis needed here). So as for explanations: 1. You understand this one. Basically it's nice to have an integral number of luma samples per line. In this case: 1/Fh * 12 3/11 MHz = 286/4.5 MHz * 12 3/11 MHz = 780 4.5 MHz is the sound carrier of the old B&W television standard which could not be changed to have the old B&W sets receive sound properly with the new color standard. But the color subcarrier needed to be in particular relation to the sound carrier and the line rate to reduce the visibility of beats between these frequencies, so the line frequency was changed . Since the B&W line freq of 15.75 kHz had a 285th harmonic at 4.489 MHz and a 286th harmonic 4.5045 MHz, and the 286th being closer to 4.5 MHz, 286 was chosen as the scale factor to derive the new color line rate from the 4.5 MHz sound carrier. 2. Given that the square pixel device of the period was a VGA monitor of 640x480 pixels, as VGA was introduced by IBM in 1987, it seems reasonable to assume that 640 was the target pixel width of the active part of a line. The active part of the NTSC line at a sample rate of 12 3/11 MHz is (1/Fh - 10.9 us) * 12 3/11 MHz = (286/4.5 MHz - 10.9 us) * 12 3/11 MHz = 646.22727 Pretty close to 640 with ~3 pixels of active video lost on each of the left and right edge. 3. & 4. The chroma subcarrier freq is fc = 4.5 MHz/286 * 455/2 ~= 3.579 MHz by design for reasons cited in  and . It is important to note that when factored, this can be written as fc = 5 MHz * (3*3)/(2*5) * (1)/(2*11*13) * (5*7*13)/2 And note that 455 was chosen because it was made up of small odd factors for various benefits and reasons listed in  and . Canceling all the terms one gets: fc = 5 MHz * 63/88 and this is the form the FCC used in its rules. Now we can make the observation that: 12 3/11 MHz = fc * (8/7) * 3 = fc * 24/7 Expanding 12 3/11 = 5 MHz * (3*3)/(2*5) * (1)/(2*11*13) * (5*7*13)/2 * (2*2*2)/7 *3 Note that the 7 cancels out the last odd factor introduced to produce "frequency interleaving" mentioned in  and . This may not be a good thing - I'm not sure. Note that 8/7 gives a "basic" highest frequency of 4.0909 MHz, which is close to the maximum frequency of 4.2 MHz of the luminance signal, and slightly above fc, but exactly cancels out factors in both the numerator and denominator of fc, to keep the relationship between 12 3/11 and fc and the line frequency simple. Note that the 3 gives a multiple of the basic frequency that is greater than the Nyquist rate for sampling the basic frequency and thus for sampling the chroma and probably luma. Does that sound close to a reasonable, original rationale, or is there too much hand waving? Regards, Andy References:  Abrahams, I. C., "Choice of Chrominance Subcarrier Frequency in the NTSC Standards", Proceedings of the I-R-E, January 1954, pp 79-80  Abrahams, I. C., "The 'Frequency Interleaving' Principle in the NTSC Standards", Proceedings of the I-R-E, January 1954, pp 81-83  Blinn, James F., "Jim Blinn's Corner: The World of Digital Video", IEEE Computer Graphics and Applications, September 1992, pp 106-112Note that some of the relevant information from the 1954 Abrahams papers that Andy referenced ( and ) is also contained in a short section of the Wiki page on NTSC.
Andy followed this up on 28 May 2008 with:
The more I think about it the more I want to refine the details of the rationale for 3 & 4. Ultimately I think some motivation was to be able to pick off a frequency easily from the frequency dividers that already had to generate the chroma subcarrier freq anyway. Also the intent had to be sampling the highest luma freq (4.2 MHz) by a factor >= 2. The chroma freq probably wasn't in the constraint; just a convenient source.
The original card designer, whose thoughts we are now trying to reverse-engineer, was in the luxurious position of being able to pick any convenient value for the luma sampling frequency that also satisfied constraint (A), (B), and (D) above.
So the designer would logically pick a multiple of the line frequency that shared many common factors with the chroma multiple 455/2, so that the chroma subcarrier frequency and the luma sampling frequency could share some of the same clocking hardware in order to reduce cost and complexity.
Andy shows that the luma sampling frequency chosen, 12 3/11 MHz, which is 780 times the line freqency, is exactly 24/7 times the chroma subcarrier frequency, which is 455/2 times the line frequency. Since 24/7 doesn't have that many prime factors, it is plausible that this is why 12 3/11 MHz was chosen.
Anyone up for that?
Or it's possible that some other reason we have yet to guess is what led the designer to choose 12 3/11. Any ideas?
So if the goal for picking a pixel sampling frequency, fs, include 1. approximately 640 active pixels per line 2. an integer multiple, N, of the horizontal line rate fh 3. most easily derived from the chroma freq, fc and since fc = fh * 455/2, it seems reasonable (but not obvious to me why) to try and pick N with as many factors in common with 455 as possible, while getting reasonably close to 640 pixels in the active portion of a line. The factors of 455 are 5, 7, and 13. The values of N, that yield close to 640 pixels, and have more than one factor in common with 455 are 735 = 3*5*7*7 => 11.5647 MHz => ~609 pixels => -4.85% diff from 640 770 = 2*5*7*11 => 12.1154 MHz => ~638 pixels => -0.32% diff from 640 780 = 2*2*3*5*13 => 12.2727 MHz => ~646 pixels => +0.97% diff from 640 805 = 5*7*23 => 12.6661 MHz => ~667 pixels => +4.21% diff from 640 So if those are the candidates, 12.1154 MHz and 12.2727 MHz are the two best. Since "not the horizontal blanking interval" isn't the best definition of the active part of a line, I suspect 12.2727 MHz was preferable, knowing that some of the 646 pixel times wouldn't actually be visible. I suppose one can quibble about what is the active portion of an NTSC line, but the Horizontal Blanking interval (HBI) is 10.9 usec +/- 0.2 usec in every book I have. So I had the spreadsheet compute the active region of a line as "not HBI", for HBI of 10.7, 10.9, and 11.1 usec.Download square-pixel-clock-options.ods (OpenDocument spreadsheet for OpenOffice/StarOffice/...)
Download square-pixel-clock-options.xls (Excel spreadsheet)
Download square-pixel-clock-options.pdf (PDF format: read-only)
I thought I'd mention some observations about VGA:Yup that's all true. I think the huge precedent of the already-existing 1987 VGA display card standard being 640x480 is already enough to explain why the computer video input card designer was choosing 640. The reasons (i) and (ii0 you gave are perhaps what had motivated IBM to choose 640x480 for CGA/EGA/VGA in the first place. The divisibility (iii) is certainly a plus on the software too (it became even more relevant on the software side when JPEG and MPEG came along).
These reasons together lead me to say that 640 pixels was the target count for active pixels per line.
- i. Its 640x480 resolution has a screen ratio of 4:3.
- ii. The active portion of an NTSC screen is about 483 lines, IIRC. That's pretty close to 480.
- iii. 640 and 480 are both divisible by 16. That's a nice property for storing and fetching pixel data in memory.
Your observation raises an important point I'm surprised I hadn't thought of before. Early personal computers like the Radio Shack TRS-80s, Commodore/Amiga, Atari 2600, Apple II, and early IBM PCs with CGA/EGA adapters were designed to hook up to consumer TVs so they very much cared about the details of NTSC scanning.
It wasn't until later graphics standards that it became widely accepted that we needed to buy separate "computer" monitors for computers rather than TVs. That is, it wasn't until later that the hardware details of the graphics card became divorced from the details of NTSC scanning. For some transitional cards like CGA, software developers had to assume that their customers might either have a NTSC composite monitor/TV, or a digital RGBI monitor:
I wonder if we look back into the history of these early computer display devices, all of which greatly predated video input cards, if we will find 12 3/11 MHz somewhere.
Perhaps the designer of the first video digitizer card was simply copying 12 3/11 from somewhere else.
Let's see if this pans out...
CGA (1981) was 640x200 and was compatible with regular TVs:
You could plug in either a composite (NTSC) monitor or a specially-built digital RGBI monitor. (CGA chose 200 in part because they knew the NTSC TV would be interlaced and they wanted to avoid or simplify dealing with field flicker!)
So far so good, but in this case we don't get any 12 3/11 MHz joy, because:
EGA (1984) was 640x350:
I believe this was the first IBM family card that could not be hooked up to an NTSC monitor: this was the first time you were forced to buy a specially-built computer monitor.
So this wouldn't help us link 640 to square-pixel scanning of an NTSC signal.
VGA (1987) was 640x480
Same deal: VGA required a special monitor.
So this wouldn't help us link 640 to square-pixel scanning of an NTSC signal.
Amiga 2000 (Released 1986) And Video Toaster first gen (released 1990)
The 640×400i resolution (720×480i with borders disabled) was first introduced by home computers such as the Commodore Amiga and (later) Atari Falcon. These computers used interlace to boost the maximum vertical resolution....The advantage of a 720×480i overscanned computer was an easy interface with interlaced TV production, leading to the development of Newtek's Video Toaster. This device allowed Amigas to be used for CGI creation in various news departments (example: weather overlays), drama programs such as NBC's seaQuest, WB's Babylon 5, and early computer-generated animation by Disney for the Little Mermaid, Beauty and the Beast, and Aladdin.
The Toaster was released as a commercial product in December 1990 for the Commodore Amiga 2000 computer system, taking advantage of the video-friendly aspects of that system's hardware to deliver the product at an unusually low cost 2399 USD. The Amiga was unique among personal computers in that its system clock at 7.16 MHz was precisely double that of the NTSC color carrier frequency, 3.579 MHz, allowing for simple synchronization of the video signal.
The Amiga [graphics] chipset can genlock — adjust its own screen refresh timing to match an NTSC or PAL video signal. When combined with setting transparency, this allows an Amiga to overlay an external video source with graphics. This ability made the Amiga popular for many applications, and provides the ability to do character generation and CGI effects far more cheaply than earlier systems
Aside from simple fades and cuts, it had a large variety of character generation, overlays, and complex animated switching effects. These effects were in large part performed with the help of the native Amiga graphics chipset which were synchronized to the NTSC video signals; the result being that while the Toaster was rendering a switching animation the computer desktop display would not be visible
Ok this is all promising, especially since the Video Toaster itself had video inputs, though at its core the Video Toaster was really an expansion card for the Amiga 2000 with BNC video in/out connectors and it acted like a video switcher---the actual video pixels did not go into the computer in any software sense or ever cross the bus of the expansion card.
So again, I don't see how this could link back to 12 3/11 MHz square sampling of NTSC. I could never find much information about this mysterious 720 pixel wide Amiga overscanned mode, but combining all the tidbits above, one can conclude that the computer-generated characters and CGI effects were probably done at a resolution of 720 wide. It's clear that 720 pixels scanned across the whole NTSC active region with 480 lines is not going to be anywhere near square. Yes, the software designers needed to know just now non-square 720 pixels were so they could render circular circles, and they also probably knew exactly how those 720 pixels would map onto the NTSC timing of the input and output video signals (because they were tightly bound to one specific Amiga hardware and so could know its behavior precisely), so the Video Toaster overall would have to have made the same kind of definitive judgment about the proper luma sampling frequency to get square pixels. But because they were working in 720, it's unlikely that we will find any precedents for 12 3/11 MHz in there.
Hmm, it seemed so promising. But maybe 12 3/11 MHz came from some other historical source.
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