# Video

A video signal is a sequence of*frames*(images) rather than a sequence of numbers. For example, view the motorcycle video (courtesy of Fox and LightStorm Entertainment). Note that the video may be painfully slow to download over a modem (it is a 628 kbyte file). The following sequence of images gives every 10-th frame (reduced in size):

The video lasts 5 seconds, and there are a total of 150 frames, so the frame rate is 30 frames per second, the same as NTSC video (the analog broadcast television standard in the U.S.) and most digital video formats.

Recall that a color image is a function

*Image*:

*VerticalSpace*×

*HorizontalSpace*→

*Intensity*

^{3},

or

*Image*:

*VerticalSpace × HorizontalSpace*→

*Colormap*,

if a colormap is used. We denote the set of all images (if we are using a colormap) by

*Images*= [

*VerticalSpace*×

*HorizontalSpace*→

*Colormap*].

Note that here, each member of the set is a function, but otherwise, this is a set like any other. A video sequence can therefore be represented as a function where the range is a set of functions,

*Video*:

*Time*→

*Images*,

where in this case *Time* = {0, 1/30, 2/30, ... } is the set of
times for each frame. This sort of function, which maps a set into a function,
is a powerful tool, one that we will exploit more fully by modeling *systems*
as functions that map function spaces into function spaces.

*Video* is a function of time. For a given time *t*,* Video*(*t*)
is a frame. We could model a video signal somewhat differently, however,
as

*AltVideo*:

*Time*×

*VerticalSpace*×

*HorizontalSpace*→

*Intensity*

^{3}

Notice that this is now not just a function of time, but of time and space.