一种改进的经验模态分解消噪阈值函数

在已有的经验模态分解（empirical modede composition，EMD）阈值消噪的基础上，提出了一种新的EMD域可导阈值函数。新阈值函数简单且便于计算，具有连续性和高阶可导性，可有效克服硬阈值EMI）消噪时和消噪后EMD系数不连续的缺点；也可有效克服软阈值EMD消噪时和消噪后EMD系数与原始EMD系数之间存在着恒定偏差的缺点。实验结果表明，经可导阈值的EMD方法消噪后，可有效减弱含噪信号突变点处的Gibbs现象，消噪后信号具有更好的视觉效果。与经典的硬闽值和软阈值EMD消噪方法相比，所提出的方法在信噪比和均方误差两方面都有较好的提高。

An improved denoising thresholding function based on empirical mode decomposition

A new differentiable thresholding function is proposed based on traditional empirical mode decomposition （EMD） thresholding functions. The proposed thresholding function is simple in expression and convenient to calculate. It is continuous and has a high order derivative. The new thresholding function can overcome the discontinuity of EMD hard thresholding func- tions. It also can overcome the defect that there is a stable dispersion between the denoised EMD coefficients and the original EMD coefficients of soft thresholding functions. The experimental results shows that, compared to the EMD hard and soft thresholding functions, the denoised signal by the proposed thresholding function has higher SNR, lower MSE and clearer visual effect. The Gibbs phenomenon near the singularities of the denoised signal is effectively weakened.