Expressing ECG wave as Fourier series

ECG (Electrocardiography) is a process of producing an electrocardiogram. It is a voltage versus time graph of the electrical activity of the heart using electrodes placed on the skin at various parts of the body.

These electrodes detect the small electrical changes that are a consequence of cardiac muscle depolarization followed by repolarization during each cardiac cycle (heartbeat).

Helps in detecting heart health issues. For people with non-erratic heartbeats, the ECG graph is quasi-periodic.

Helps in detecting heart health issues. For people with non-erratic heartbeats, the ECG graph is quasi-periodic.

This can be used to measure the heart rate of the patient. Also, if such a clear peak is not observed, then the heart-rate is implied to be erratic

Changes in the normal ECG pattern occur in numerous cardiac abnormalities, including cardiac rhythm disturbances (such as atrial fibrillation and ventricular tachycardia), inadequate coronary artery blood flow (such as myocardial ischemia and myocardial infarction), and electrolyte disturbances (such as hypokalemia and hyperkalemia).

Graph of ECG
  1. The normal human pulse rate is anywhere between 70 to 72 beats per minute but for simplifying the calculations, we take the pulse rate to be 60 beats per minute as a minute has 60 seconds, so the time period becomes 1s or 1000ms.
  2. We assume that the ECG signal only consists of triangular and parabolic waveforms only

β€’ The P wave is caused by contraction of the right atrium followed by the left atrium (the chambers at the top of the heart). It is parabolic and follows 𝑓 (𝑑) = βˆ’π‘Žπ‘‘^2 + 𝑏𝑑 + 𝑐

  • The QRS complex represent the point in time when most of the heart muscles are in action, so has highest amplitude. This uses two equations: for QR, it is 𝑓 𝑑 = 𝑑 and for RS, it is 𝑓 (𝑑) = βˆ’π‘‘
  • The T wave represents the polarization of the ventricles (the chambers at the bottom of the heart).This portion can also be modelled as a parabolic function with 𝑓(𝑑) = βˆ’π‘‘π‘‘ 2 + 𝑒𝑑 + f
a0 coefficient of Fourier Series
Equation for an coefficient of Fourier Series
an coefficient of Fourier Series
Equation of bn coefficient of Fourier Series
bn coefficient of Fourier Series
Equation of the entire Fourier Series

Heart illnesses are a major problem for people of all ages and we should have a robust mechanism for detecting them beforehand so that maximum lives can be saved, hence we have found some illnesses which can be detected after modelling them with Fourier series and some of the

Tachycardia β€” A heart condition where the heart rate goes up resulting in the isoelectric line on the ECG graph to shorten

Brachy cardia β€” A heart condition where the heart rate goes down, resulting in the isoelectric line on the ECG graph to elongate

Source Code

Github Profile

Website

A data science enthusiast currently doing bachelor's degree in data science