Abstract
The frequency characteristics of wavelets and the vanishing moments of wavelet filters are both important parameters of wavelets. Clarifying the relationship between the wavelet frequency characteristics and the vanishing moments of the wavelet filter can provide a theoretical basis for selecting the best wavelet. In this paper, the frequency characteristics of wavelets were analyzed by mathematical modeling, the mathematical relationship between wavelet frequency characteristics and vanishing moments was clarified, the optimal wavelet base function was selected hierarchically according to the amplitude frequency characteristics of ECG signal, and an accurate notch filter was realized according to the frequency characteristics of the noise. The experimental results showed that the optimal orthogonal wavelet analysis for the ECG signals with different frequency characteristics could make the high frequency energy distribution sparser, and the method proposed in this paper could effectively preserve the singularity of the signal and reduce the signal distortion.
Highlights
How to select and use the appropriate wavelet basis function and how to filter the noise of the specific frequency characteristic in the process of wavelet transform[6]
Based on the above discussion, the two key steps of the wavelet-based denoising algorithm proposed in this paper are as follows: First, the amplitude-frequency characteristic of the ECG signal is analyzed to determine the wavelet loss moment order, and on this basis, the optimal wavelet basis function is selected for different levels of wavelet decomposition
The adaptive genetic algorithm based on EEMD (Genetic EEMD), the adaptive threshold denoising algorithm based on discrete wavelet transform (Threshold DWT) and the wavelet denoising algorithm which is optimized by this paper (Proposed DWT) are applied for filtering processing
Summary
For ECG signal analysis and processing by wavelet transform, there are several purposes: denoising, feature detection, and data compression. Wavelet vanishing moment and filter amplitude-frequency characteristics. Theorem 1: The order of the vanishing moment of an orthogonal wavelet is proportional to its corresponding filter order. ( ) ( ) ftIihnltetehsrteselteorpapenersatithtietohnselobepadnegdoefot41fhπ6teh≤eedtωgrea
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