Frequency-domain design of 2-D state-space digital filters using adaptive LMS algorithm

An adaptive technique is developed for designing two-dimensional (2-D) state-space digital filters in the frequency domain. The Roesser local state-space (LSS) model is used to describe the 2-D digital filters. First, the frequency response of the Roesser LSS model is investigated to define a performance index in which the reference signal is specified by magnitude response and group delays in the pass-band. An iterative algorithm based on the least mean square (LMS) method is then presented together with the calculation of gradient vectors required in the adaptive process. Finally, two numerical examples are solved to illustrate the utility of the proposed technique.