todo



ECG SIMULATION USING MATLAB

Principle of Fourier Series
























Presented by
R. KARTHIK
B.E. (E.C.E), 6TH Semester
College of Engineering, Guindy,
Anna University,
Chennai – 600025
e-mail: may_62003@yahoo.co.in



Introduction:
The aim of the ECG simulator is to produce the typical ECG waveforms of different leads and as manyarrhythmias as possible. My ECG simulator is a matlab based simulator and is able to produce normal lead II ECG waveform.

The use of a simulator has many advantages in the simulation of ECG waveforms. First one is saving of time and another one is removing the difficulties of taking real ECG signals with invasive and noninvasive methods. The ECG simulator enables us to analyze and study normal andabnormal ECG waveforms without actually using the ECG machine. One can simulate any given ECG waveform using the ECG simulator.

Significant features of ECG waveform:
A typical scalar electrocardiographic lead is shown in Fig. 1, where the significant features of the waveform are the P, Q, R, S, and T waves, the duration of each wave, and certain time intervals such as the P-R, S-T, and Q-Tintervals.


fig 1.Typical ECG signal

Main features of this simulator:
Any value of heart beat can be set
Any value of intervals between the peaks (ex-PR interval) can be set
Any value of amplitude can be set for each of the peaks
Fibrillation can be simulated
Noise due to the electrodes can be simulated
Heart pulse of the particular ECG wave form can be represented in a separate graphPrinciple:
Fourier series
Any periodic functions which satisfy dirichlet’s condition can be expressed as a series of scaled magnitudes of sin and cos terms of frequencies which occur as a multiple of fundamental frequency.
∞ ∞
f (x) = (ao/2) + Σ an cos (nπx / l) + Σ bn sin (nπx / l),
n=1n=1

ao = (1/ l ) ∫ f (x) dx , T = 2l -- (1)
T

an = (1/ l ) ∫ f (x) cos (nπx / l) dx , n = 1,2,3…. -- (2)
T

bn = (1/ l ) ∫ f (x) sin (nπx / l) dx , n = 1,2,3…. -- (3)T

ECG signal is periodic with fundamental frequency determined by the heart beat. It also satisfies the dirichlet’s conditions:
Single valued and finite in the given interval
Absolutely integrable
Finite number of maxima and minima between finite intervals
It has finite number of discontinuities
Hence fourier series can be used for representing ECG signal.Calculations:
If we observe figure1, we may notice that a single period of a ECG signal is a mixture of triangular and sinusoidal wave forms. Each significant feature of ECG signal can be represented by shifted and scaled versions one of these waveforms as shown below.
QRS, Q and S portions of ECG signal can be represented by triangular waveforms
P, T and U portions can be represented by triangularwaveforms
Once we generate each of these portions, they can be added finally to get the ECG signal.
Lets take QRS waveform as the centre one and all shiftings takes place with respect to this part of the signal.

How do we generate periodic QRS portion of ECG signal












Fig 2. generating QRS waveform
From equation (1), we have

f(x) = (–bax/l) + a 0 < x < ( l/b )= ( bax/l) + a (– l/b)< x < 0

ao = (1/ l ) ∫ f (x) dx
T
= (a/b) * (2 – b )


an = (1/ l ) ∫ f (x) cos (nπx / l) dx
T
= ( 2ba / (n2π2 )) * ( 1 – cos (nπ/b))


bn = (1/ l ) ∫ f (x) sin (nπx / l) dx
T
= 0 ( because the waveform is a even function)...