Existence and numerical stability analysis of the sine function in denoising source separation

Denoising Source Separation (DSS) is a critical technique in signal processing for extracting source signals from noisy mixtures. Traditional DSS algorithms rely on the hyperbolic tangent function (tanh(s)) as the nonlinear transformation to maximize non-Gaussianity, but this function often suppresses high-frequency components and exhibits a rapidly decaying derivative, limiting its effectiveness for sub-Gaussian signals. In this paper, we propose replacing tanh(s) with the sine function (sin(s)) in DSS and provide rigorous theoretical proofs of its existence as an optimal nonlinearity and the numerical stability of the resulting algorithm, termed DSS-sin. We demonstrate that sin(s) enhances non-Gaussianity more effectively due to its oscillatory derivative (cos(s)∈[-1,1]) and favorable Taylor expansion properties. Additionally, we integrate the Maximum Overlap Discrete Wavelet Transform (MODWT) for post-separation denoising, reducing reconstruction errors and improving noise robustness. Simulations confirm that DSS-sin outperforms the conventional DSS-tanh approach in terms of separation performance and calculation speed.