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The authors study some speech enhancement algorithms based on the iterative Wiener filtering method due to Lim and Oppenheim (1978), where the AR spectral estimation of the speech is carried out using a second-order analysis. But in their algorithms the authors consider an AR estimation by means of a cumulant (third- and fourth-order) analysis. The authors provide a behavior comparison between the cumulant algorithms and the classical autocorrelation one. Some results are presented considering the noise (additive white Gaussian noises) that allows the best improvement and those noises (diesel engine and reactor noise) that leads to the worst one. And exhaustive empirical test shows that cumulant algorithms outperform the original autocorrelation algorithm, specially at low SNR.