13.5 MHz

This is the sampling frequency of luminance in SD digital television systems as defined by the ITU. It is represented by the 4 in 4:2:2. The use of the number 4 is pure nostalgia as 13.5 MHz is in the region of 14.3 MHz, the sampling rate of 4 x NTSC color subcarrier (3.58 MHz), used at the very genesis of digital television equipment.

Reasons for the choice of 13.5 MHz belong to politics, physics and legacy. Politically it had to be global and to work for both 525/60 (NTSC) and 625/50 (PAL) systems. The physics is the easy part; it had to be significantly above the Nyquist frequency so that the highest luminance frequency, 5.5 MHz for 625-line PAL systems, could be faithfully reproduced from the sampled digits i.e. sampling in excess of 11 MHz but not so high as to produce unnecessary, wasteful amounts of data. Some math is required to understand the legacy.

The sampling frequency had to produce a static pattern on both 525 and 625-line standards, otherwise it would be very complicated to handle and, possibly, restrictive in use. In other words, the frequency must be a whole multiple of the line frequencies of both standards.

The line frequency of the 625/50 system is simply: 625 x 25 = 15,625 Hz
(NB 50 fields/s makes 25 frames/s)
So line length is 1/15,625 = 0.000064 or 64µs

The line frequency of the 525/60 NTSC system is complicated by its offset factor of 1000/1001 to avoid interference when transmitted. The line frequency is 525 x 30 x 1000/1001 = 15,734.265 Hz. This makes line length 1/15,734.265 = 63.5555µs

The difference between the two line lengths is 64 – 63.55555 = 0.4444µs

This time divides into 64µs exactly 144 times, and into 63.5555µs exactly 143 times. This means the lowest common frequency that would create a static pattern on both standards is 1/0.4444 MHz, or 2.25 MHz.

Now, back to the physics. The sampling frequency has to be well above 11 MHz, so 11.25 MHz (5 x 2.25) is not enough. 6 x 2.25 gives the adopting sampling frequency for luminance of 13.5 MHz.

Similar arguments have been applied to the derivation of sampling for HD. Here 74.25 MHz (33 x 2.25) is used for luminance sampling.

See also: 1.125 MHz4:1:1, 4:2:0, 4:2:2, 4:4:4, 4fsc, Nyquist (frequency)