A Design Method for 3-D FIR Cone-Shaped Filters Based on the McClellan Transformation

This paper presents an efficient technique for designing three-dimensional (3-D) finite-impusle-response (FIR) digital filters having cone-shaped magnitude response. The McClellan transformation method is used as basis of the design. The new approach proposes a closed form solution for the transform coefficients of the mapping function. A simultaneous determination of the 1-D cutoff frequency of the prototype filter is also considered. The newly obtained relations for the transform parameters are very simple and depend on the angle of inclination of the cone. Additionally, the analytical expressions for the impulse response coefficients of the transformation subfilter are also derived. The behavior of the transformation function is examined, followed by several detailed examples with different input specifications of designed 3-D cone filters.