Asymptotic region of stability of digital filters represented by y[i] = Ay [i − 1] + By[i − N − 1] + x[i]

In this paper an investigation of the stability region of digital filters defined by y[i] = Ay[i − 1] + By[i − N − 1] + x[i], where x[.] is the input, y[.] is the input, A and B are real constants, and N is a non-negative integer is presented. It is demonstrated that the region of stability on the A–B plane possesses symmetries whose nature depend on whether the value of N is odd or even. The asymptotic (as N tends to infinity) region of stability is found to be enclosed by the four lines defined by |A| + |B| < 1. Simultation results are presented verifying the analysis.