3-D FIR Cone-Shaped Filter Design by a Nest of McClellan Transformations and Its Variable Design

In this paper, the technique of a nest of McClellan transformations is proposed for the design of 3-D FIR cone-shaped filters. First, a transformation subfilter for fan-type mapping is found. Then the cosine term of a frequency variable of the above transformation subfilter is replaced by an embedded transformation subfilter which possesses circular contours. The technique stated above is also extended to design 3-D FIR variable cone-shaped filters such that the inclination of the cone-shaped filters can be adjusted online. Moreover, an efficient structure is proposed for the implementation of the designed filters. Several examples will be presented to demonstrate the effectiveness of the proposed method.