The classical receptive fields of simple cells in mammalian primary visual cortex demonstrate three cardinal response properties: 1) they do not respond to stimuli which are spatially homogeneous; 2) they respond best to stimuli in a preferred orientation (direction); and 3) they do not respond to stimuli in other, non-preferred orientations (directions). We refer to these as the Balanced Field Property, the Maximum Response Direction Property, and the Zero Response Direction Property, respectively. These empirically-determined response properties are used to derive a complete characterization of elementary receptive field functions defined as products of a circularly symmetric weight function and a simple periodic carrier. Two disjoint classes of elementary receptive field functions result: the balanced Gabor class, a generalization of the traditional Gabor filter, and a bandlimited class whose Fourier transforms have compact support (i.e., are zero-valued outside of a bounded range). The detailed specification of these two classes of receptive field functions from empirically-based postulates may prove useful to neurophysiologists seeking to test alternative theories of simple cell receptive field structure, and to computational neuroscientists seeking basis functions with which to model human vision.