 That is, if the above relation is satisfied for some "f", "g", and A, it must also be satisfied for the same "f" and "g′" and A′ given by

formula_9

formula_10

where B is a non-singular "M × M" matrix, since

formula_11

An "N" variable function which has intrinsic dimension "M < N" has a characteristic Fourier transform.Intuitively, since this type of function is constant along one or several dimensions its Fourier transform must appear like an impulse (the Fourier transform of a constant) along the same dimension in the frequency domain.Let "f" be a two-variable function which is i1D.