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

• Acrobat PDF format, 169137 bytes