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The paper presents a new normalized least mean fourth (NLMF) algorithm. The algorithm is derived through the minimization of the mean fourth normalized estimation error. The main advantage of the algorithm with respect to the available NLMF algorithms is that it remains stable as the input power of the adaptive filter increases. A stability step size bound of the proposed algorithm is derived. The step size bound depends on the weight initialization, while it does not depend on the input power of the adaptive filter. Simulation results support the analytical results of the paper.

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