Stability and convergence of a class of nonlinear algorithms in digital signal processing

Square-root algorithms have use in certain areas of digital signal processing. However, they are characterized as being non-linear in nature and hence their analysis is not straight-forward. This paper examines two such algorithms and shows that the convergence is guaranteed provided the closed-loop discrete-time system is stable, but that the upper limit on stability is determined by the values of the square-root coefficients themselves. The analysis is quite classical but also requires a link between Toeplitz matrices and polynomials to progress further.