On the synthesis of space dependent transfer functions

A method to synthesize the space dependent transfer functions of a class of dynamic systems from the frequency response data is presented. The systems that give rise to space dependent transfer functions are those which may be represented by partial differential equations in which the space and time dependences of the dependent variables are not separable. The method consists of representing the system transfer function as a series of suitable space modes with frequency dependent coefficients. The resulting synthesis procedure is straightforward and is applicable to many practical cases of interest. The method is applicable to both minimum and nonminimum phase transfer functions.