2.2 Connection between Signals and Systems

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17

Blood pressure

in mmHg

Volume

in ml

120

100

80

60

40

20

0

130

90

50

ECG

Systole

Diastole

Aorta

Atrium

PCG

Venticle

Fig. 2.8: Vital signals of a human heart: Sequence of three heart cycles in the electrocardiogram

(ECG), phonocardiogram (PCG) and the corresponding pressure sequence in the left ventricle and the

aorta (centre), as well as the ventricular volume (bottom).

ricle will be delayed, resulting in a change in the ECG signals. Thus there exist a more

or less pronounced connection between the signal-generating system "heart" and the

respective biosignal. In mathematical modelling, this signal-system-relation is called

sensitivity of a state variable (or measured variable) of the system to the change of a

physical system parameter (e.g. the conductivity of the conduction system). In signal

processing, such dependencies are made clear with the help of correlation. As will be

shown later in the book in subsection 2.3.6, one speaks of a strong/weak correlation

of the signal quantities.

One of the main concerns of biosignal processing is the analysis and diagnostic

use of these signal-system correlations. Due to the complexity and variability of liv-

ing systems, the correlations are usually not clear, not pronounced enough, incom-

plete, or covered by artefacts and affected by uncertainties. Mathematical models are

helpful in searching, as they greatly improve the basic understanding of the system

interrelationships. For example, model systems can be parameterised by exact quant-

ities and their synthetic signals can be analysed possessing the "ground truth". Of-

ten, new signal-system-coherences or signal components are found which could not

yet be measured on the physiological system for technical reasons (for example, due

to unsuitable sensors or measurement locations, too low time resolution, too strong

artefacts or filtering of the signals, etc.). A combination of mathematical modelling,

sensitivity analysis and adaptation of the measurement technology and evaluation

algorithms often proves to be very profitable in the search for the correct parameters

or measured variables in the biosignal.