Editing Walsh function (section)

==Comparison between Walsh functions and trigonometric functions==

Walsh functions and trigonometric functions are both systems that form a complete, [[orthonormality|orthonormal]] set of functions, an [[orthonormal basis]] in the [[Hilbert space]] <math>L^2[0,1]</math> of the [[square-integrable function]]s on the unit interval. Both are systems of [[bounded function]]s, unlike, say, the [[Haar wavelet|Haar system]] or the Franklin system.

Both trigonometric and Walsh systems admit natural extension by periodicity from the unit interval to the [[real line]]. Furthermore, both [[Fourier analysis]] on the unit interval ([[Fourier series]]) and on the real line ([[Fourier transform]]) have their digital counterparts defined via Walsh system, the Walsh series analogous to the Fourier series, and the [[Hadamard transform]] analogous to the Fourier transform.