Design of multidimensional FIR digital filters using the symmetrical decomposition technique

A technique for the design of multidimensional FIR filters based on symmetrical decomposition is described. Along with this technique, a procedure to decompose a frequency response into symmetrical components is also discussed. It is proved that the design based on the symmetrical decomposition technique when the cost function is chosen as the weighted square error yields the same optimal solution as the classical method that does not use the decomposition technique. The l₂ norm design is discussed as a special case of weighted l₂ norm design. It is also shown that the decomposition technique is advantageous when the weight function satisfies some symmetry properties. Examples are also provided to illustrate the application and the effectiveness of applying the decomposition in the design of 2-D and 3-D FIR filters