• If we denote by D the distance between the spatial centers of a basis formed by these functions, and the distance between their centers of support in the frequency domain as W, then the basis is complete (and the representation is an invertible transform) if WD = 2pi [2].

• It has been shown [3] that these functions achieve the lower limits of uncertainty imposed by the Heisenberg uncertainty inequalities.

• It has also been demonstrated [3-7] that the Gabor functions agree reasonably well with receptive field profiles measured for simple cells in the cat striate cortex.

• This transform is not, however, orthogonal. The most obvious consequence of this is that the transform coefficients cannot be calculated by simply computing the inner products of the basis functions and the signal of interest (or, equivalently, by convolving with the basis functions and subsampling).