中文摘要：

小波消失矩阶数的不同,对应的小波滤波器的幅频曲线也不相同,因此选用不同的小波滤波器对信号进行滤波,去噪效果会有明显差异。本文通过数学建模研究分析小波滤波器的幅频特性,明确小波幅频特征及与小波滤波器消失矩的阶数之间的关系,为选择最优小波滤波器提供理论依据。本文提出针对ECG噪声的频率特点实现精确陷波去噪,有效的保留了信号的奇异点与特征值,减少了信号失真。实验结果表明,选择具有相对最优消失矩阶数的提升小波滤波器对ECG进行去噪处理,可以使信号能量分布更加集中,去噪效果更好。

英文摘要：

Different orders of vanishing moments of the wavelet, the amplitude-frequency curve of the corresponding filters may be different too, so using different wavelet filters for de-noising on the ECG signal, the denoising effect will be signifi-cantly different. In this paper, we study the amplitude frequency characteristics of wavelet filter by building the mathemati-cal model and clarify the relationship between the wavelet amplitude characteristic and the order of the vanishing moment of the wavelet filter, and try to provide the theoretical basis for selecting the optimal wavelet filter. In this paper, we proposed a special method to realize the accurate notch denoising based on the frequency characteristics of ECG noise, which effec-tively preserves the singularity and feature of the signal and reduces the signal distortion. The experimental results show that the lifting wavelet filters with the relative optimal order of the elimination moment can make the signal energy distribution more concentrated and the denoising effect more better.