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