The set of orthonormal functions employed in calculating the terms of a transform of the kind exemplified by the Fourier transform and the Walsh transform (see Walsh analysis): the orthonormal basis of the Fourier transform consists of the imaginary exponential functions, and that of the Walsh transform consists of the Walsh functions.

In order to calculate the terms of a transform effectively, the basic functions must be orthogonal but need not also be normal (orthonormal). Such a non-normalized basis is called an orthogonal basis. The calculation of the transform terms is correspondingly called orthonormal analysis or orthogonal analysis. Such analysis is only possible if there are sufficient functions in the set to form a basis: such a set is called a complete set of functions.