vector or set of coefficients of a finite impulse response filter u03bb 1 for ideal conditions no measurement noise no quantization noise deterministic and statistically stationary acoustic inputs discrete frequency components in x k and infinite precision arithmetic under these ideal conditions the filter coefficients converge to those required to minimize the mean squared error e k algorithms for selecting parameter u03bc k appear in the literature and modifications or embodiments of published u03bc k selection algorithms appear in various prior art however the choice of parameters u03bb and u03bc k as presented in the prior art does not guarantee stability of the traditional lms algorithm under non ideal real world conditions in which measurement noise in the microphone signals is present finite precision effects reduce the accuracy of numerical computations and noise fields are highly nonstationary furthermore in current algorithms the leakage parameter must be selected so as to maintain stability for worst case i e nonstationary noise fields with impulsive noise content resulting in significant noise cancellation degradation parameter u03bb is a constant between zero and one choosing u03bb 1 results in aggressive performance with compromised stability under real world conditions choosing u03bb lt 1 enhances stability at the expense of performance as the algorithm operates far away from the optimal solution the invention disclosed here is a computational method based on a lyapunov tuning approach and its embodiment that automatically tunes time varying parameters u03bb k and u03bc k so as to maximize stability with minimal reduction in performance under noise conditions with persistent or periodic low signal to noise ratio low excitation levels and nonstationary noise fields the automatic tuning method provides for time varying tuning parameters u03bb k and u03bc k that are functions of the instantaneous measured acoustic noise signal.