Merging individual waves into a single wave as a synthetic ECG

Hello everyone :)

I created individual ECG waves (P wave, QRS complex, and T wave, which is identical to the P wave) using symbolic variables and the Fourier series. However, I am struggling to merge these waves into a single waveform—it jumps around unpredictably, and I generally don’t know how to proceed. :(

my code is here:

close all;clear all; clc;

%P wave (T wave)

T = 1

f = 1/T

omega = 2*pi*f

syms t k

c=0

a_0 = (1/pi) * int((-t^2), t, c, c + 1);

a_n = (1/pi)*int(-t^2 * cos(k*t),t,c,c+1);

b_n = 0;

FS_P = a_0/2 + symsum(a_n*cos(k*t)+b_n*sin(k*t),k,1,1)

FS_P = 4*FS_P

four = subs(FS_P)

%number of repetitions

N = 1

ezplot(four,0:6.3*N)

grid on

%QRS complex - first part

syms t k x

c=0

a_0 = 0

a_n = 0

b_n = 1/pi * int(t*sin(k*t),x,c,c+2*pi)

FS_QRS = a_0/2 + symsum(a_n*cos(k*t)+b_n*sin(k*t),k,1,1000)

FS_QRS = 2*FS_QRS

four = subs(FS_QRS)

N=4

ezplot(four)

%QRS complex - second part

syms t k x

c=0

a_0 = 0

a_n = 0

b_n = 1/pi * int(-t*sin(k*t),x,c,c+2*pi)

FS_QRs = a_0/2 + symsum(a_n*cos(k*t)+b_n*sin(k*t),k,1,1000)

FS_QRs = -2*FS_QRs

four = subs(FS_QRs)

ezplot(four)

I try to simply add these signals but it doesnt work :(

Answer 1

[Aravind]

Hi @Tomas,

To combine the individual ECG components (P wave, QRS complex, and T wave) into a single waveform, you need to properly align these components in time and ensure they are accurately scaled. Here's a general approach to do this:

1) Define Each Component: Ensure each wave component is defined over its specific time interval, as the P wave, QRS complex, and T wave occur at different times during a cardiac cycle.

2) Time Shifting: Introduce a time shift for each wave to appear in sequence rather than overlapping or jumping. You can apply time shifts to each component using the "subs" function, like this: "subs(FS_component, t, t - shift_amount)". For more information on the "subs" function, visit: https://www.mathworks.com/help/symbolic/sym.subs.html. In the ECG cycle, the P wave is first with no time shift, followed by the QRS complex, and then the T wave. To achieve the time shifting, you might do something like:

% Example for time shifting
P_wave = subs(FS_P, t, t - 0);  % Starts at t = 0
QRS_complex1 = subs(FS_QRS1, t, t - 1);  % Shifted to start at t = 1

3) Scaling: Ensure the P wave, QRS complex, and T wave are scaled appropriately, as ECG components have different amplitudes and durations.

4) Combine the Waves: After scaling and shifting, sum the waveforms to create the complete ECG waveform.

% Combine the wave components
ECG_waveform = P_wave + QRS_complex1 + QRS_complex2;

Additionally, consider experimenting with the number of terms in the Fourier series to balance accuracy and computational efficiency.Incorporating these factors should help you successfully combine the different waves to generate a synthetic ECG waveform.

I hope this answers your question.