 This means that there exists a normalized vector formula_12 and a one-variable function "g" such that

formula_13

for all formula_14.If "F" is the Fourier transform of "f" (both are two-variable functions) it must be the case that

formula_15

Here "G" is the Fourier transform of "g" (both are one-variable functions), "δ" is the Dirac impulse function and m is a normalized vector in formula_16 perpendicular to n. This means that "F" vanishes everywhere except on a line which passes through the origin of the frequency domain and is parallel to m. Along this line "F" varies according to "G".Let "f" be an "N"-variable function which has intrinsic dimension "M", that is, there exists an "M"-variable function "g" and "M × N" matrix A such that

formula_17

Its Fourier transform "F" can then be described as follows