A Novel Approach for Testing Stability of 1-D Recursive Digital Filters Based on Lagrange Multipliers

Digital filters have found their way into many products from every day consumer items such as mobile phones to advanced maritime and military communications and avionics systems. Design of digital filters faces two fundamental problems, their stability and synthesis. Recursive filters have more stability problems than nonrecursive filters. Stability of a filter can be determined by the location of the zero valued region of the denominator polynomial of its transfer function. Stability of recursive filters has been studied by many researchers for the past three decades. Several theorems on stability testing and stabilizing recursive digital filters have been already proposed. We present a new approach to test the stability problem of the one-dimensional (1-D) recursive digital filters using Lagrange Multipliers. This method not only tests the stability of recursive digital filters, but also provides the stable version of the filterʹs transfer function if found to be unstable.