Efficient fast design of three- and higher-dimensional FIR digital filters by analytical least squares method

An effective method is proposed for designing three- and higher-dimensional FIR digital filters in this paper. The method is based on deriving the closed-form matrix Called by the inverse frequency response transformation matrix, such that the filter's coefficients can be computed directly from the given specifications without any iterative procedures and optimization techniques. Design examples are presented to demonstrate the flexibility and the efficiency of the method, and it is shown that even the filter's lengths up to 21 x 21 x 21 only 0.4 s CPU time is needed.