FFT Analysis,denoising And Filtering Of ECG Signal
Steps involved 1 Reading ECG signal 2) Change input signal from time domain to frequency domain(FFT analysis) 3) Filter the signal in frequency domain using Savitzky-Golay filter 4)Convert step (3) to time domain 5)Obtain the performance parameter of step (3) using the following mathematical tools... I) Signal to noise ratio (SNR) II) Mean square Error (MSE) III) Signal to Interference Ratio (SIR)
Kshitij Singh answered .
2025-11-20
Function Plot ATM.m
function [val x] = plotATM(Name)
% usage: plotATM('RECORDm')
%
% This function reads a pair of files (RECORDm.mat and RECORDm.info) generated
% by 'wfdb2mat' from a PhysioBank record, baseline-corrects and scales the time
% series contained in the .mat file, and plots them. The baseline-corrected
% and scaled time series are the rows of matrix 'val', and each
% column contains simultaneous samples of each time series.
%
% 'wfdb2mat' is part of the open-source WFDB Software Package available at
% http://physionet.org/physiotools/wfdb.shtml
% If you have installed a working copy of 'wfdb2mat', run a shell command
% such as
% wfdb2mat -r 100s -f 0 -t 10 >100sm.info
% to create a pair of files ('100sm.mat', '100sm.info') that can be read
% by this function.
%
% The files needed by this function can also be produced by the
% PhysioBank ATM, at
% http://physionet.org/cgi-bin/ATM
%
% plotATM.m O. Abdala 16 March 2009
% James Hislop 27 January 2014 version 1.1
infoName = strcat(Name, '.info');
matName = strcat(Name, '.mat');
Octave = exist('OCTAVE_VERSION');
load(matName);
fid = fopen(infoName, 'rt');
fgetl(fid);
fgetl(fid);
fgetl(fid);
[freqint] = sscanf(fgetl(fid), 'Sampling frequency: %f Hz Sampling interval: %f sec');
interval = freqint(2);
fgetl(fid);
if(Octave)
for i = 1:size(val, 1)
R = strsplit(fgetl(fid), char(9));
signal{i} = R{2};
gain(i) = str2num(R{3});
base(i) = str2num(R{4});
units{i} = R{5};
end
else
for i = 1:size(val, 1)
[row(i), signal(i), gain(i), base(i), units(i)]=strread(fgetl(fid),'%d%s%f%f%s','delimiter','\t');
end
end
fclose(fid);
val(val==-32768) = NaN;
for i = 1:size(val, 1)
val(i, :) = (val(i, :) - base(i)) / gain(i);
end
x = (1:size(val, 2)) * interval;
%plot(x', val');
for i = 1:length(signal)
labels{i} = strcat(signal{i}, ' (', units{i}, ')');
end
%legend(labels);
%%xlabel('Time (sec)');
% grid on
end
Main.m
%%
clc;
[val, x] = plotATM('100m');%%PlotAtm is function used for reading ecg file
%%
h=val(1,:);%% selection of ecg signal for further process
%%
Fs=360;%% sampling frequency given
t=(0:length(h)-1)/Fs;%% time for the signal
figure;
plot(t,h)%% plotting
title('Original ECG signal in time domain')
%%
u=length(h);%% calculating length of signal
K=abs(fft(h));%%converting into frequency domain
fax_bins = [0 : u-1]; %frequency axis in bins
u_2 = ceil(u/2);
figure;
plot(fax_bins(1:u_2), K(1:u_2))
xlabel('Frequency (Bins)')
ylabel('Magnitude');
title('ECG in frequency domain signal (Single-sided Magnitude spectrum (bins))');
axis tight
ylim([0 200])
%%
%%
rd = 9;
fl = 21;
smtlb = sgolayfilt(h,rd,fl);
figure;
subplot(2,1,1)
plot(t,h)
%%
title('Original in time response')
grid
subplot(2,1,2)
plot(t,smtlb)
title('Filtered using Savitzky-Golay in time response')
grid
%%
rd1 = 9;
fl2 = 21;
smtlb1 = sgolayfilt(K(1:u_2),rd1,fl2);%Smooth the signal by applying a Savitzky-Golay filter of polynomial order 9 to data frames of length 21.
figure;
subplot(2,1,1)
plot(K(1:u_2))
title('Original in frequency response')
grid
subplot(2,1,2)
plot(smtlb1)
title('Filtered in Savitzky-Golay frequency response')
grid
%% butterworth filter
o=5;%% coffiecient
[b,a]=butter(o,[50 150]/360); %%[b,a] = butter(n,Wn) returns the transfer function coefficients of an nth-order lowpass digital Butterworth filter with normalized cutoff frequency Wn.
butter_filter=filter(b,a,K(1:u_2));
figure;
subplot(2,1,1)
title('Original EcG in frequency domain')
plot(K(1:u_2))
subplot(2,1,2)
plot(butter_filter)
title('filtering using butterworth in frequency domain')
%%
o1=1;
[b1,a1]=butter(o1,[1 10]/180,'Bandpass');
butter_filter1=filter(b1,a1,h);
figure;
subplot(2,1,1)
plot(t,h)
subplot(2,1,2)
plot(t,butter_filter1)
title('filtering using butterworth in time domain')
%%
%%
for i=1:length(h)
SIR=h(i)/(h(i)-smtlb(i));
end
fprintf('Signal to interference when Savitzky-Golay is applied is--- %f\n',SIR);
%%
for i=1:length(h)
SIR2=h(i)/(h(i)-butter_filter1(i));
end
fprintf('Signal to interference when butterworth filter is applied is--- %f\n',SIR2);
%%
mse=0;
for i=1:length(h)
mse=mse+(smtlb(i)-h(i))^2;
end
mse=mse/length(h);
fprintf('mean squared error original ecg signal and filtered signal(Savitzky-Golay) %f\n',mse);
%%
%%
mse1=0;
for i=1:length(h)
mse1=mse1+(butter_filter1(i)-h(i))^2;
end
mse1=mse1/length(h);
fprintf('mean squared error original ecg signal and filtered signal(butterworth Filter) %f\n',mse1);
%%
num=0;
den=0;
for i=1:length(h)
den=den+(smtlb(i)-h(i))^2;
end
for i=1:length (h)
num=num+h(i)^2;
end
SNR = 20*log10(sqrt(num)/sqrt(den));
fprintf('signal to noise ratio between original ecg signal and filtered signal(Savitzky-Golay) %f db\n',SNR);
%%
num1=0;
den1=0;
for i=1:length(h)
den1=den1+(butter_filter1(i)-h(i))^2;
end
for i=1:length (h)
num1=num1+h(i)^2;
end
SNR = 20*log10(sqrt(num1)/sqrt(den1));
fprintf('signal to noise ratio between original ecg signal and filtered signal(butterworth filter) %f db\n',SNR);
%%