A video system should ideally satisfy the principle of superposition; in other words, it should exhibit linearity. A function f is linear if and only if (iff):

The function f can encompass an entire system: A system is linear iff the sum of the individual responses of the system to any two signals is identical to its response to the sum of the two. Linearity can pertain to steady-state response, or to the system's temporal response to a changing signal.

Linearity is a very important property in mathematics, in signal processing, and in video. But linearity in one domain cannot be carried across to another domain if a nonlinear function separates the two. An image signal usually originates in a sensor that has linear response to physical intensity. And video signals are usually processed through analog circuits that have linear response to voltage or digital systems that are linear with respect to the arithmetic performed on the codewords. But a video camera applies a nonlinear transfer function - gamma correction - to the image signal. So the image signal is in a linear optical domain, and the video signal is in a linear electrical domain, but the two domains are not the same.

Excerpted from Chapter 1, Basic Principles, of A Technical Introduction to Digital Video. (New York: John Wiley & Sons, 1996). Page 17. This chapter is available online, in Acrobat PDF format.

See also: Gamma FAQ - Linear and nonlinear coding

Charles Poynton
Copyright © 1998-03-12