## Sine-Waves and Orthogonal Functions

A set of functions is orthogonal if none of the functions can be made
up from linear combinations of the others. The set of sine-waves of
different frequencies is orthogonal.
A good analogy is with *red*, *green*, and *blue*
light. However you vary the quantities, you cannot make *red*
from any mixture of *green* and *blue*. But with all
three colours, you can make any colour you like.

Similarly, by mixing sine-waves of every frequency in the right
proportions, we can construct any arbitrary function.

Back to Fourier Theory.