Design of low sensitive 2-D analog and recursive digital filters with prescribed magnitude and group delay specifications

In this paper, necessary and sufficient conditions are given, under which a two-variable rational function can be realized as the transfer, function of a doubly-terminated cascade of s1and s2-variable lossless two-ports, each two-port with all of its transmission zeros at the origin or infinity. Using the above conditions, transfer function of a 2-variable analog reference filter is generated. Parameters of this transfer function are used as parameters of optimization to minimize the least mean square error between the amplitude response of the desired and designed filters. It is shown that the method can also be modified to incorporate the phase and magnitude response of the 2-D filters. To illustrate the method, examples are given.