Purpose: Wavelet denoising is one of the denoising methods commonly used for ECG signals. However, due to the frequency overlap between the EMG and ECG, the feeble characteristics of ECG signals exists the risk of being weakened in the process of filtering noise. This paper presents a method of modified wavelet design and applies it to the denoising of ECG signals.

Materials and methods: The optimized filter coefficients are obtained by approximating the amplitude-frequency response of the ideal filter, and the wavelet is constructed with the optimized filter coefficients. The algorithm is tested by clinical ECG data.

Results: The results show that the proposed denoising method can remove the high-frequency noise effectively and enhance the characteristic information of P waves and T waves, and retain the characteristic information of the atrial fibrillation signals simultaneously. Compared with db4 and sym4 wavelets, the proposed wavelet can improve the signal to noise ratio and reduce the mean square error effectively at the same time.

Conclusion: The modified wavelet design method proposed in this paper can effectively remove high-frequency noise while retaining and enhancing weak features. It provides a theoretical guidance for the de-noising of ECG signals in mobile medicine and also provides a way for other types of weak feature signal denoising.

目的：小波降噪是ECG信号常用的降噪方法之一。然而，由于EMG和ECG之间的频率重叠，ECG信号的微弱特性存在在过滤噪声的过程中被削弱的风险。本文提出了一种改进的小波设计方法，并将其应用于心电信号的去噪。

材料和方法：通过近似理想滤波器的幅频响应获得优化的滤波器系数，并使用优化的滤波器系数构建小波。该算法通过临床ECG数据进行测试。

结果：结果表明，所提出的去噪方法可以有效地消除高频噪声，增强P波和T波的特征信息，同时保留房颤信号的特征信息。与db4和sym4小波相比，所提出的小波可以同时提高信噪比并有效降低均方误差。

结论：本文提出的改进的小波设计方法可以有效地消除高频噪声，同时保持并增强弱特征。它为移动医学中的ECG信号降噪提供了理论指导，也为其他类型的弱特征信号降噪提供了一种方法。