This paper describes a novel application of Fourier descriptor techniques for the recognition of hand gesture trajectories. Appearance based coordinates of hand centroids and time steps are normalized to a fixed length by multirate techniques. Fourier techniques are applied to the data to produce frequency domain data that is scale and translation invariant. The results of inputting the complex harmonic data to a probabilistic neural network for gesture classification are discussed. An understanding of underlying structure of gesture trajectories can be gained from modeling them as an infinite set of ellipses at given orientations. The rotation of the ellipses is visualized in the time domain as 'elliptic corkscrews'.