The design and application of a high quality three dimensional linear trajectory filter

A method is introduced for the design of 3D linear trajectory (LT) recursive digital filters which ideally have bowl-shaped passbands in the frequency domain. The passband approximation is obtained by adding the transfer functions of two 3D filters having elementary wedge-shaped passbands. The 3D elementary wedge filters are in turn obtained by applying a frequency-domain transformation to a highly selective 2D continuous-domain prototype fan filter. The design method is straightforward, computationally nonintensive, and leads to a guaranteed stable LT filter having a directional selectivity that is ideally independent of the spatial area occupied by the LT object. This advantage is demonstrated by means of a typical 3D LT filtering example.<>