Theoretical analysis of musical noise in nonlinear noise reduction based on higher-order statistics

In this paper, we review a musical-noise-generation analysis of nonlinear noise reduction techniques with using higher-order statistics (HOS). Recently, an objective metric based on HOS to analyze nonlinear artifacts, i.e., musical noise, caused by nonlinear noise reduction techniques has been proposed. Such metric enables us to perform objective comparison of any nonlinear methods from the perspective of the amount of musical noise generated. Furthermore, such metric enables us to control the musical noise generated by nonlinear noise reduction techniques. In the paper, first, the mathematical principle of the analysis for the amount of musical noise based on HOS is described, and analyses and comparison examples of typical nonlinear noise reduction techniques are demonstrated. Next, it is clarified that to find a fixed point in HOS leads to no-musical noise property in noise reduction. Finally, several expansions on the theory are discussed.