One view of the input signal illustrated above in figure 4.2, is that it is made up of a number of contributing signals - mathematically, we can consider any reasonable set of orthogonal signals as components, but the easiest ones to use are sine functions.

One extreme case often used to illustrate this is the square wave signal. In figure 4.4, we show a square wave. If this was made out of a number of sine waves with different frequencies, the contribution of each frequency would be as illustrated in figure 4.5.

The way then that we build up the square wave *constructively* out
of a set of sine waves of different frequenies can be seen in the
progression of figures,

It may seem odd that a simple ``on-off'' signal takes a lot of
contributions, but then the point is that this method of representing
the continuous signal is general, and can represent *any*
input signal.

Input data can be transformed in a number of ways to make it easier to apply certain compression techniques. The most common transform in current techniques is the Discrete Cosine Transform. This is a variant of the Discrete Fourier Transform, which is in turn, the digital (discrete) version of the Continuous Fourier Transform.

As described earlier, any signal (whether a video or audio signal) can
be considered a periodic wave. If we think of a sequence of sounds,
they are a modulation of an audio wave; similarly, the scan over an
image or scene carried out by a camera conveys a wave which has
periodic features in time (in the time frame of the scene, as well as
over multiple video frames in the moving picture). It is possible
to convert from the original signal as a function of time, to the *
fourier series*, which is the sum of a set of terms, each being a
particular *frequency* (or wavelength). You can think of these
terms or coefficients as being the *contribution* of a set of base pure
``sine-wave'' frequencies (also known as the spectral density), that
together make up the actual signal.

where *K*_{1} = 1

and

where
*K*_{1} = *pi* / 2

You can imagine these sweeping through a typical audio signal as shown in figure 4.10, and ``pulling out'' a spectrum (see figure 4.11, or set of coefficients that represent the contribution of each frequency to that part of the signal strength.