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5 Methods for Discrete Processing and Analysis of Biosignals

heart rate

50Hz Power humming

Fig. 5.19: The ECG with a 50 Hz mains hum shows the time domain (top) and the corresponding spec-

trum (bottom). At 50 Hz, a distinct spectral line of over 200 µV can be seen due to the 50 Hz mains

hum (simulation result was generated using LTspice).

also as a function of other variables, e. g. the frequency f or z := e^j2πfT. With this

representation in the "image domain", e. B. in f or z, disturbing signal components

such as e. B. the 50 Hz mains hum, border areas or a baseline fluctuation as well as

shifts are easier to recognise than in the time domain. It can therefore be used as an

important basis for filter design.

In Figure 5.19, for example, the section of an ECG is shown above, which is dis-

turbed by a sinusoidal oscillation; the corresponding representation in the frequency

domain is shown below. Here it is very clearly visible that the heart rate (first larger

spectral line) is at 1 Hz, i.e. the pulse has a value of 60 beats per minute. Further-

more, it can be seen that there is a distinct spectral line at 50 Hz, which is due to the

influence of a 50 Hz mains hum. In the time domain (above), this disturbance can

also be recognised, but its nature cannot be determined so well, which is better in the

frequency domain. Since the spectral components of the 50 Hz interference are relat-

ively far away from the frequency range of the ECG, they could be well suppressed by a

bandstop with a centre frequency of 50 Hz, if its bandwidth is narrow enough so that

no ECG components are lost.

For a linear time-invariant system, the impulse response can be used in the time

domain to determine the output signal using discrete convolution. This is often much

easier when determining the output signal for a given input signal in the "image do-