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1 Introduction to Biosignal Processing

ECGs (over 24 h), modern methods are indispensable, as a heart beats approximately

80,000 to 100,000 times during this time. In this order of magnitude, the search for ab-

normal heartbeats such as cardiac arrhythmias or unusual changes such as ventricu-

lar fibrillation presents doctors with a practically impossible task. In addition to the

precious time that would be involved in manual review, there would be a lapse of at-

tention and thus a loss of important events – not to mention the compilation of stat-

istics.

However, large amounts of data are not only generated in the analysis of intens-

ive care data, but also in telemedicine. The variety of data in the field of commercial

sports medicine has grown rapidly through the use of mobile technologies and soft-

ware on smartphones, as has the continuous monitoring of older people to monitor

their health. The list of possible vital signs and health parameters besides ECG is long:

blood pressure, heart rate, blood oxygen saturation, body weight and temperature –

all require conscientious and contextual evaluation with mathematical methods to

guide diagnosis. With their help, the essential parameters are to be found automatic-

ally and the physician is to be pointed to relevant contents. Especially when monitor-

ing patients in intensive care units or in telemedicine, threatening conditions should

be detected quickly and reliably and the treating staff should be informed by an alarm.

The problem with this form of automatic detection of important events is to de-

velop a reliable algorithm with high accuracy –an almost impossible task given the

diversity of patients and the variability in the signals. In other words, algorithms must

be applicable to all possible variants of a given signal. This so-called robustness of an

algorithm is an essential feature in the subsequent approval as a medical device. In

addition, the measurement technology and algorithms must be absolutely insensit-

ive to external electromagnetic interference to which a measurement setup may be

exposed.

Mathematical methods and the development of software are therefore indispens-

able components of biosignal analysis. The success of modern monitoring systems

therefore comes only to a small extent from the development of electronic hardware –

the far greater contribution to the success of an innovative product is now made by

intelligent signal evaluation. For example, in addition to exclusive filtering in the fre-

quency or time domain, interfering signals are nowadays increasingly analysed us-

ing the wavelet transformation in the time-frequency domain, since it allows the best

possible time and frequency resolution for a given signal section. The detection of im-

portant signal sections in an ECG signal course, for example, requires the extraction

of statistically robust features, which are then fed to a classifier or a neural network

for analysis. With this method, a large number of anomalies in ECGs can already be

reliably distinguished today.

Model-based techniques such as the "Kalman" filter or "Markov" models are also

used to detect abnormal (pathological) states and the associated changes in state.

Early detection of trends or random fluctuations in a signal course, such as signal vari-

ations shortly before an epileptic seizure in the electroencephalogram (EEG), using