Design of 3-D planar and beam recursive digital filters using spectral transformation

A spectral transformation technique is proposed for the design of three-dimensional (3-D) recursive digital filters having planar and beam frequency responses. Circuit-theoretic concepts are used to generate stable 3-D continuous domain networks from a corresponding one-dimensional (1-D) prototype network. Implementation schemes are developed in the discrete domain that convert the 3-D analog network into a 3-D wave digital filter (WDF). The proposed 3-D discrete beam and planar filters offer significant advantages over direct-form realizations including the low-sensitivity properties of the WDF and simplicity of the structure.<>