6.3 Signals of the Cardiovascular System

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Nowadays, of course, more powerful hardware can be used. The development engin-

eer can design the algorithm on the PC and also test it in hardware by coupling it to

the PC in real time. Hardware today does not always have to be built in the lab to be

tested. An intensive simulation with PC hardware-coupling shortens the development

enormously. The exact structure for simulating the Pan-Tompkins-algorithm, as it can

be realised e.g. in Matlab/Simulink or Scilab/Xcos, is shown Figure 6.22. Of course, it

is also possible to write programs in Matlab or Scilab, C or Fortran, but the graphical

representation is often much easier to understand than a complicated program where

after years even the developer has difficulties to understand his program.

Pre-filtering

An analogue low-pass filter first limits the magnitude frequency spectrum to 50 Hz.

This serves to comply with the sampling theorem when subsequently sampling at

200 Hz.¹⁰

Bandpass Filtering

In the next step, the ECG, which is available in digitised form, is additionally bandpass

filtered in the discrete-time domain. Since most of the energy of the QRS complex lies

between about 5 to 15 Hz [77], a bandpass in the range of 5 to 11 Hz is chosen. In this

range, however, a bandpass is difficult to realise with various methods. Therefore, it

is designed as a series circuit of a low-pass and a high-pass. The low pass has easily

realisable coefficients,

ATP(z) =

(1 −z⁻⁶)

2

(1 −z⁻¹)^{2 ,}

mit

|ATP(ωTa)| = ^{sin2(3 ωTa)}

sin²(ωTa/2)

,

(6.11)

a cut-off frequency of 11 Hz and a gain of 36 (cf. Figure 6.23).

Its group delay is constant 5 samples. This corresponds to 5 ⋅(1/200 Hz) = 25 ms

for a sampling frequency of 200 Hz. Because of

ATP(z) = ^YTP(z)

XTP(z) ^,

XTP, YTP : input-, output spectrum

(6.12)

is further obtained with Equation 6.11:

YTP(z) ⋅(1 −2z⁻¹ + z⁻²) = XTP(z) ⋅(1 −2z⁻⁶ + z⁻¹²)

(6.13)

and after transforming back to the time domain, the corresponding algorithm for the

output signal yTP(n) as a function of the input signal xTP(n):

yTP(n) = 2yTP(n −1) −yTP(n −2) + xTP(n) −2xTP(n −6) + xTP(n −12) .

(6.14)

10 The upper cut-off frequency must be less than half the sampling frequency.