Stability Analysis And PLSI Based Design Of Stable And Optimal Two-Dimensional Recursive Digital Filters - Gnanamuthu, Ezra Morris (2007)
Designing stable two-dimensional recursive digital filters is very important in the field of Digital Signal Processing. The general method of designing a stable filter is to design the filter first without worrying about the stability and then stabilize it without altering the magnitude spectrum if the designed filter is found to be unstable. Based on the Shanks' conjecture that the planar least square inverse (PLSI) of the given arbitrary 2-D polynomial is stable, the unstable filter is stabilized by replacing the denominator polynomial of the filter by its double PLSI polynomial. Unfortunately the Shanks' conjecture has not been proved yet and there are many unresolved issues in stabilizing unstable filters using PLSI method.