Error spectrum shaping in three-dimensional recursive digital filters

Error spectrum shaping is considered in 3-D recursive digital filters. A technique is developed for obtaining the optimal error feedback (EFB) coefficients that minimize the noise variance at the filter output. A detail discussion on the use of symmetry and antisymmetry of the EFB coefficients is also presented. The proposed technique relies on the use of the Lagrange's multiplier method. Moreover, the suboptimal EFB with integer coefficients is constructed by using a least-squares discrete-space optimization algorithm. Finally, a numerical example is given to illustrate the utility of the proposed technique.