In this paper, we propose a new theoretical analysis of amount of musical noise generated in several noise reduction methods with a decision-directed a priori SNR estimator using higher-order statistics. In our previous study, a musical noise assessment based on kurtosis has been successfully applied to spectral subtraction and Wiener filter. However, this approach cannot be applied to some high-quality noise reduction methods, namely, the minimum mean-square error short-time spectral amplitude estimator, the minimum mean square error log-spectral amplitude estimator and the maximum a posteriori estimator, because such methods include the decision-directed a priori SNR estimator, which corresponds to a nonlinear recursive (infinite) process for noise power spectral sequences. Therefore, in this paper, we introduce a computationally efficient higher-order-moment calculation method based on generalized Gauss-Laguerre quadrature. We also mathematically clarify the justification of using a typical decision-directed parameter, namely, magic number 0.98, in the three types of the decision-directed-based estimators from a viewpoint of amounts of musical noise and speech distortion. In addition, we perform comparison between these noise reduction methods based on the mathematical analysis and human perception test.
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