A Comparative Study of Stability Testing Approaches of Two-Dimensional Recursive Digital Filters

There are many problems in science and engineering whose solution is applied in the design of Multi-Dimensional (MD) digital filters. Digital filtering finds an important position in the field of digital signal and image processing. Recently there had been a great deal of interest in the design and stability analysis of Two-Dimensional (2-D) recursive digital filters. The design techniques for stable One Dimensional (1-D) digital filters are relatively well developed; but their extension to 2-D had been tried with difficulties. The stability problem of 2D filters had been the subject of intensive research during the recent decades. The trend is towards finding sufficient conditions, because necessary and sufficient conditions are difficult to find or to test. In this study, we make a detailed comparison of the various approaches available for testing the stability of 2-D recursive digital filters. Though researchers had done a lot on the stability testing methods, a comparative study by listing the computational complexities of various methods had not been done so far. This study would help the researchers to choose proper stability testing methods based on the computational complexities.