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.