💥1 概述
本文使用集成经验模式分解和希尔伯特变换的R峰值检测（心脏频率）进行心电图信号去噪。
该项目的目的是通过使用集成经验模式分解的新方法（一种去噪生物信号的新方法）来过滤和去噪生理信号（在这种情况下，选择心脏信号心电图）。此外，使用希尔伯特变换来记录心脏频率。
📚2 运行结果
🎉3 参考文献
[1]张勇,王介生.基于多分辨率分析的心电图信号去噪算法[J].系统工程与电子技术,2002(12):32-34.
👨💻4 Matlab代码
主函数部分代码：
%Final Project. Biosignals processing. %EMD denoising and R peak detention of ECG signal using Hilbert Transform. clear all; close all; clc; %% Data Loading ecg=load ('ecg1.mat'); % loading the signal ecg=struct2cell(ecg); ecg=cell2mat(ecg); ecg = (ecg - 1024)/200; % you have to remove "base" and "gain" ecg1=ecg(1,:); %Noisy ecg ecg2=ecg(2,:); %filtered ecg Fs =500; % sampling frequecy t =linspace(0,length(ecg1)/Fs,length(ecg1)); %time vector %% ECG signal denoising imf=eemd(ecg1,.2,70); %Apply the EEMD to the noisy signal .2->ratio of the standard deviation 70->ensemble number imfs=imf'; %transpose the imf's matrix reconstruction=imfs(4,:)+imfs(5,:)+imfs(6,:); %We consider that these 3 imf's possess the important information %4 order Butterworth filter bandpass .05-230Hz. fclowpass=230; % Low pass cut-off frequency 230Hz fchighpass=.05; % Low pass cut-off frequency .05Hz filterorder=4; %filter order [b,a]=butter(filterorder,[filterorder*fchighpass/Fs,2*fclowpass/Fs]); filtered_ECG=filter(b,a,reconstruction); %% Emphasizing R peaks of the ECG %Getting the maxima and minima of the ECG signal, to emphasize the R peaks decg=(1/Fs)*(diff(filtered_ECG)); %derivative of the ecg hecg=hilbert(decg); %hilbert transform of the derivative. envelope=abs(hecg); %It returns the envelope of the ecg %% R peaks detection maximum=(max(envelope)); Threshold=.6*(maximum); [pks,locs] = findpeaks(envelope,'MinPeakHeight',Threshold); time=(1/Fs)*length(ecg1); timefactor=60/time; cardiacFreq=round(timefactor*length(pks)); %% Plots figure (1) plot(t,ecg1); xlabel('time (s)'); ylabel('mV'); title('Raw ECG'); figure(2) subplot(7,1,1); plot(t,imfs(1,:)); xlabel('time (s)'); ylabel('mV'); title('Original ECG'); subplot(7,1,2); plot(t,imfs(2,:)); xlabel('time (s)'); ylabel('mV'); title('1st IMF'); subplot(7,1,3); plot(t,imfs(3,:)); xlabel('time (s)'); ylabel('mV'); title('2nd IMF'); subplot(7,1,4); plot(t,imfs(4,:)); xlabel('time (s)'); ylabel('mV'); title('3rd IMF'); subplot(7,1,5); plot(t,imfs(5,:)); xlabel('time (s)'); ylabel('mV'); title('4th IMF'); subplot(7,1,6); plot(t,imfs(6,:)); xlabel('time (s)'); ylabel('mV'); title('5th IMF'); subplot(7,1,7); plot(t,imfs(7,:)); xlabel('time (s)'); ylabel('mV'); title('6th IMF'); figure (3) subplot(7,1,1); plot(t,imfs(8,:)); xlabel('time (s)'); ylabel('mV'); title('7th IMF'); subplot(7,1,2); plot(t,imfs(9,:)); xlabel('time (s)'); ylabel('mV'); title('8th IMF'); subplot(7,1,3); plot(t,imfs(10,:)); xlabel('time (s)'); ylabel('mV'); title('9th IMF'); subplot(7,1,4); plot(t,imfs(11,:)); xlabel('time (s)'); ylabel('mV'); title('10th IMF'); subplot(7,1,5); plot(t,imfs(12,:)); xlabel('time (s)'); ylabel('mV'); title('11th IMF'); subplot(7,1,6); plot(t,imfs(13,:)); xlabel('time (s)'); ylabel('mV'); title('12th IMF'); subplot(7,1,7); plot(t,imfs(14,:)); xlabel('time (s)'); ylabel('mV'); title('13th IMF'); figure (4) plot(t,reconstruction); xlabel('time (s)'); ylabel('mV'); title('IMFs reconstruction'); figure(5) plot(t,filtered_ECG); xlabel('time (s)'); ylabel('mV'); title('Filtered ECG (IMF+bandPass)'); figure(6) plot(t(1:9999),decg); xlabel('time (s)'); ylabel('d(ECG)/dt'); title('ECG derivative'); figure(7) plot(t(1:9999),hecg); xlabel('time (s)'); ylabel('H(d(ECG)/dt)'); title('Hilbert Transform of derivate'); figure(8) plot(t(1:9999),envelope); xlabel('time (s)'); ylabel('B(d(ECG)/dt)'); title('Envelope'); figure (9) plot(t(1:9999),envelope,locs,pks,'or'); legend('ECG','R peaks','Location','NorthWest');
