Theoretical Analysis of Musical Noise Generation in Noise Reduction Methods with Decision-Directed a Priori SNR Estimator

In this paper, we propose a new theoretical analysis of the 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. However, this approach cannot be applied to some high-quality noise reduction methods, e.g., Ephraim-Malah's minimum mean-square error short-time spectral amplitude (MMSE STSA) 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 MMSE STSA estimator from a viewpoint of amounts of musical noise and speech distortion.