5.3 Methods for Analysis and Processing of Discrete Biosignals

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time-continuous signal and then resampled with a higher sampling frequency.

An additional analogue-to-digital converter is therefore unnecessary.

Averaging of signals

The time averaging of signals is used on the one hand for low-pass filtering and on

the other hand for separating the deterministic and stochastic signal components of

a biosignal. A biosignal can thus be described as

s(k) = μ(k) + Σ(k)

(5.32)

where μ(k) contains the transient mean, i.e. the deterministic part, and Σ(k) contains

the stochastic part.

For example, if s(k) is the sampled biosignal, the averaged signal sM(k) is obtained

when averaging over N + 1 samples:

sM(k) = ¹

N

N

∑

i=0

f(k −i) ,

N: filter order.

(5.33)

Such averaging filters can be easily realised by a non-recursive digital filter N-th order

whose coefficients ci, for i = 0, . . . , N all have the same value 1/N (see Figure 5.35).

Due to the averaging over the window width, the sampled signal experiences a time

base modified by 1/N, i.e. the sampling frequency becomes lower.

In addition to this average filtering over several continuous function values

through a windowing, there is also the possibility of averaging over the entire sig-

nal course of several signals. For example, if one has sampled several periods of a

signal, these can be averaged by cutting out coherent. In this case, one obtains a

mean value and an associated variance or standard deviation for each sample of

the signal. The mean value curve describes the deterministic part of the biosignal,

whereby all deviations are expressed in the variance. It is thus possible to find the

noise component and outliers and to separate them from the biosignal, since these

components behave stochastically and are therefore averaged out during summation.

With periodic signals, a fundamental distinction is made between coherent and

non-coherent averaging. In practice, for example, in the analysis of EEG signals, the

usually very small evoked potentials are separated from the dominant noise com-

ponent with the help of a triggered non-coherent averaging of many signals. But the

method can also be used to determine a characteristic signal course of an often re-

peated EMG measurement for a certain body movement or to determine the pulse wave

course of a photoplethysmogram.

The Listing 5.3.1.1 shows a Matlab script for a coherent averaging of a N-times

measured, noisy signal S1(n) = {s1(n)}, . . . , SN = {sN(n)}, in the corresponding Fig-

ure 5.12 the associated spectrum and the course of the signal-noise-ratio as a function

of N are shown next to the signals.