## A
Tutorial on Magic Numbers for High Definition Electronic Production

### Abstract

Numerical parameters for television systems must be selected to meet
constraints imposed by the various disciplines of television: mechanics,
analog and digital electronics, magnetics and even optics. Television system
parameters have sometimes been selected based on the technology of the day.
For example, the FCC decided in 1953 to modify the frame rate of NTSC by
the factor 1000/1001 upon the introduction of colour. Although appropriate
in a world without videotape recording, this decision did not adequately
anticipate the development of technology. The burden of drop-frame timecode
was unwittingly imposed: many television equipment designers and users still
face the associated hassles on a daily basis, even twenty seven years later.
The FCC leaves a heritage of magic numbers: 7, 11 and 13, the factors of
1001. The mystical - some say unlucky - properties of these particular numbers
were well known in ancient times. The magic of highly composite numbers
and simple integer ratios allows implementation optimizations.

We have thirty or so years of experience in selecting numerical parameters
for video systems, with both good and bad results. This paper describes
how we can take advantage of this experience to develop a rational standard
for high definition electronic production.

I presented this paper at the 132nd *SMPTE Technical Conference*,
October 13-17, 1990, in New York. It was published by SMPTE as Preprint
No. 132-119.

### Complete paper

Charles - Articles

1997-03-05