Appendix G: 270 Million—A Magic Number in Digital Video
The SDI link carries uncompressed SD video at 270 Mbps line rates. Interestingly, the SDI link can synchronously carry a digitally sampled 625/25 line structure signal (used in the PAL system) or the 525/29.97003 line structure signal (used in NTSC systems) at the same line rate of 270 Mbps. How is this possible, because the two TV systems have apparently unrelated sampling rates? History records that the 525 and 625 analog systems were developed independently of each other. However, the two digital systems have a common sampling rate of 270 Mbps. Let us see why.
In the 625 line system the horizontal line rate is 625 × 50/2 = 15,625 lines per second (LPS, units in hertz). In the 525 line system, the LPS rate is 525 × 60/2 × 1,000/1,001 = 15,734.2657734. Do the two line rates have a common relationship? By examining these two values, we get the following factorizations:
• 56 = 15,625 (PAL)
• (7 × 25 × 3) × 30 × (125 × 8)/(7 × 11 × 13) = 15,734.265 … (NTSC)
• Dividing the second value by the first yields an exact integer ratio of 144/143. This relationship was not planned by the respective PAL/NTSC system designers, yet is of great benefit to us. Now, 144 × 15,625 Hz = 143 × 15,734.265 Hz = 2.25 MHz and this is the lowest common frequency from which both line rates can be derived. How may this value be used? All digitally sampled systems have a corresponding sample clock. This clock needs to be high enough (meet the Nyquist sample rate rules) to faithfully represent any analog video signal in digital form yet not be so high as to waste bandwidth and storage space. Given the bandwidth of SD video signals, a factor of 6 was deemed ideal, yielding a system sample clock of 6 × 2.25 MHz 13.5 MHz. This is the basic sampling rate of SD digital video.
It turns out that each image RGB pixel set can be represented by a color difference component format. This digital format is referred to as Y’CrCb (luma and two chroma samples). Y’CrCb is derived from RGB pixels via mathematical operations, albeit with some loss of image resolution. The SDI data structure format (component video mode) carries the Y’CrCb signal with 4:2:2 sampling. There is one Y’ value and one chroma (either Cr or Cb) value per RGB sample set on average.1 SDI supports 10-bit samples, so the luma/chroma sequence requires 2 × 10 bits. The overall SDI line rate is 13.5 MHz × 20 bits = 270 Mbps. This rate is usable for both 625 and 525 line TV systems. So indeed, 270,000,000 is a magic number in SD digital video systems.
One more point of interest: the ratio 144/143 between the 525 and the 625 systems is also a measure of the spatial/temporal information content difference between the two systems. One has more spatial resolution (625/25), whereas the other has more temporal resolution (525/29.97). As humans, we value both spatial and temporal quality when viewing a moving image. There are, of course, countless levels of nuance when evaluating image attributes, but at a high level it is apparent that the two systems’ “image quality” differs by only 0.7 percent if the spatial and temporal resolutions are weighted equally.
1 If this all sounds confusing, see Chapter 11 for more information on the Y’CrCb and 4:2:2 formats and their use in video systems.