Abstract: The method of adaptive noise cancelling (ANC) can efficiently enhance signals corrupted by additive noises.Since the traditional ANC which uses LMS transversal filter (TFA-NC) has its drawbacks,we have studied in this thesis the ANC using the lattice joint process estimator (LFANC).It has been shown that LFANC possesses excellent convergence properties inde-pendant of the input.We have found theoretically an analytical formula about the misadjustment of LFANC,from which the results obtained are quite close to those from experiments,showing the important conclusion that misadjustment of LFANC increases exponentially with the number of stages of the filter.We have also succeeded in using optimized step size in multistage LFANC,as a result the convergence has been speeded up drastically and almost no extra computation is needed.In applying the optimal step size LFANC to real noise speech processing,good results have been obtained.