ECG signal denoising using Ensemble Empirical Mode Decomposition and R peak detection (cardiac frequency) using Hilbert Transform.
The aim of this project is to filter and denoise a physiological signal (in this case I opted for cardiac signals ECG), by using a new approach of Ensemble Empirical Mode Decomposition (a novel approach for denoising biological signals). Moreover, to register the cardiac frequency by using Hilbert Transform.
*Axcor----To obtain the correlation index of signals. Optional to use, to compare between signals after applying a filter.
*ecg.mat---Real ecg example #1.
*ecg1.mat---Real ecg example #2.
*eemd.m--- EEMD function. See the description below.
*EEMDdenosisingHilbert.m---Main source code. The file to run. It has the implementation of the functions with the ecg signals.
*emax--Returns the max points and their coordinates
*emin--Returns the min points and their coordinates
*extrema--this function ususally used for finding spline envelope (not used).
*peakseek---It finds the peaks in a certain scope (not used, because Hilbert Transform is more accurate).
Example:
ecg=load ('ecg1.mat'); % loading the signal
ecg=struct2cell(ecg);
ecg=cell2mat(ecg);
ecg = (ecg - 1024)/200; % you have to remove "base" and "gain"
https://github.com/benpolletta/HHT-Tutorial/blob/master/HuangEMD/eemd.m#L12
HHT-Tutorial/HuangEMD/eemd.m (GITHUB)
References:
Wu, Z., and N. E Huang (2008),
Ensemble Empirical Mode Decomposition: a noise-assisted data analysis method.
Advances in Adaptive Data Analysis. Vol.1, No.1. 1-41.
code writer: Zhaohua Wu. footnote:S.C.Su 2009/03/04
The EEMD descompose the signals into Intrinsic Mode Functions, which a few are taken to reconstruct the signal and remove noise and artifacts. To apply the EEMD function:
Example:
imf=eemd(ecg1,.2,70); %Apply the EEMD to the noisy signal
Arguments: ecg1:signal to be filtered .2->ratio of the standard deviation, 70->ensemble number
These values where set according to literature.
To filter the signal I apply a 4th order digital butterworth bandpass and the eemd.
%% 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);
The Hilbert Transform is used to Emphasize the R peaks of the ECG and to have one unique r peak, as it was previously removed the noise and the artifacts.
The image depicts the initial raw physiological signal and the final filtered signal with the respective R peaks (cardiac Frequency), including the Hilbert Transform.
The following image shows the filtered/denoised ECG signal (Without the Hilbert Transform).
