Given the above definition, it is sometimes convenient to look at the
values of all the channels of a stream at a given time. This is
exactly what a frame is. For a given stream 
, the function 
is defined as:
Note that in the above, 
is used, but any other
could just as easily have been used.
Intuitively, a frame represents a ``slice'' of each of the channels at a given point in time. It represents the values of each of a channel for a given time t.
The connection between channels, frames and streams is illustrated in
figure 4.1. In this diagram, we have three channels
, 
and 
, with the range of the first two being
the real numbers, and the range of the last being 
. The
stream consists of these three channels together. The ``length'' of
the stream is 24 time-slices; in other words it consists of 24 frames.
Each frame has three channels, and the domain of the function
in this case is [0..23]. A frame is a ``vertical
slice'' of the stream, for example, frames 13 and 17, each slice
indicating the values of the channels at a given time. On the other
hand, a channel is a ``horizontal slice'' of the stream, indicating
the variation of some feature over time.
Figure 4.1: The relationship between channels, frames and
streams.