576i PAL colour subcarrier

The numbers 768 and 512 were convenient for early memory systems: 512 is the ninth power of 2, and 768 is 3 times the eighth power of 2. In the early days of digital television, this combination – 768 and 512 – led to very simple memory and addressing circuits for framestores. The importance of this special combination of 768 and 512 is now irrelevant: Framestore systems today have well ovver a single frame of memory; memory devices have much higher capacities; and total memory capacity is now a more important constraint than active sample and line counts. In any case, the binary numbers 768 and 512 were never any help in the design of 576i framestores.

Common sampling rate

The designers of the NTSC and PAL systems chose video parameters based on simple integer ratios. When component digital sampling became feasible it came as a surprise that the ratio of line duration of 480i and 576i systems turned out to be the ratio of 144 to 143, derived as shown in Table 32.1.

Table 32.1 Derivation of 13.5 MHz common sampling rate

The lowest common sampling frequency corresponding to these factors is 2.25 MHz, half of the nowfamiliar NTSC sound subcarrier frequency of 4.5 MHz. Any multiple of 2.25 MHz could have been used as the basis for line-locked sampling of both 480i and 576i. The most practical sampling frequency is 6 times

2.25 MHz, or 13.5 MHz; this multiplier is a compromise between a rate high enough to ease the design of analog antialiasing filters and low enough to minimize data rate and memory requirements.

Figure 32.1 Numerology of HD scanning

HD was originally conceived at NHK as having twice the horizontal and twice the vertical resolution of conventional television: At the top right is the conceptual origin of the total number of HD scanning lines as twice the geometric mean of 525 and 625. North America would have preferred twice 525 and Europe twice 625. The designers choose a total line count of

Incidentally, 2000/1125 equals 16/9. 1125 (i.e., 53× 32), a compromise that was thought to be politically acceptable on both sides of the Atlantic

Ocean.

Underneath the scanning designations 525/60, 625/50, and 1125/60 in Figure 32.1 is a grey bar containing the ratio of image rows to total scanning lines in each system. The count of lines per total vertical (LT) for each of these systems is the fraction 23⁄25 (92%) of the total. This led to NHK’s original choice of 1035 image rows for 1125/60 HD.

The desire for a common sampling frequency for component digital video led to the synthesis of line rates of 480i and 576i into a common sampling frequency, 13.5 MHz, and a common count of samples per active line (SAL), 720. For HD, the active pixel count was doubled to increase the horizontal resolution; then multiplied by the 4⁄3 increase in aspect ratio (from 4:3 to 16:9), netting 1920.

An image array having dimensions 1920× 1035 results from these choices, and SMPTE standardized that as 240M in 1988. However, in about 1991 it became clear that the 1920× 1035 structure had

a sample pitch unequal in the horizontal and vertical dimensions – nonsquare sampling. The degree of inequality was small – just 4% – but for many applications any departure from equal spacing imposes

a burden. In about 1995, the standard was adapted to achieve square sampling by choosing a count of image rows 9⁄16 times 1920, that is, 1080 rows. SMPTE, and subsequently ATSC, enshrined square sampling in the 1920× 1080 image array. The system has about two million pixels per frame; the exact number is very slightly less than 221, a neat fit into binary-sized memory components.

NHK planned to operate the 1920× 1035 system at a frame rate of exactly 30 Hz (“30.00 Hz”) and early 1035i equipment operated only at that rate. However,

the discrepancy of about one frame time every 33.367 seconds between 1035i30.00 and 480i29.97 is a big nuisance in standards conversion. To ease this problem, and to ease engineering difficulties associated with digital audio sample rates, 1080i HD standards accommodate both 29.97 Hz and 30 Hz frame rates.

While NHK and others were developing 1125/60 interlaced HD, progressive-scan systems having nearly identical pixel rate were being developed by other organizations, mainly in the United States. The technology of the day permitted a pixel rate of about

60 megapixels per second, whether scanning was interlace or progressive. With interlace scanning, 60 Mpx/s at 30 Hz frame rate allows a two-megapixel image structure. With progressive scanning, 60 Mpx/s at

60 Hz frame rate allows just one megapixel. Partitioning one megapixel into a square lattice yields an image structure of 1280× 720; this led to the 720p family of standards.

In the mid-2000s, the digital cinema community took advantage of HD equipment and infrastructure, and adopted 1080 image rows for the “2 K” standard. However, 2048 image columns were chosen. That choice produced a new aspect ratio, about 1.896, never before used for movies. The standard 1.85 cinema aspect ratio would have been achieved with 1998 image columns, but apparently some members of the community were fearful that 1998 could not be claimed to be “2 K.” The choice of a number somewhat greater than 1920 seems to be motivated by the short term desire to distinguish digital cinema from HD, politically if not technically. The 64 additional pixels on each edge can hardly be argued as increasing resolution. Super-HD has been demonstrated with 2·1920 or 3840 image rows, but “4 K” D-cinema has 4096 image columns. Ultra-HD is proposed with 4·1920 or 7680 image rows but presumably “8 K” D-cinema will offer 8192. It seems to me that the divergence of the 2K·1920 HDrelated image formats and the power-of-two D-cinema formats can’t be sustained. HD formats, leveraging

a connection to consumer volumes, are likely to win in the end.