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5 Methods for Discrete Processing and Analysis of Biosignals

Fig. 5.8: Sub-sampling, omitting every second sample and using a low-pass beforehand to ensure

compliance with the sampling theorem.

moments such as the expected value or the variance, as well as the interrelationships

of two curve progressions with the help of the covariance or the correlation. Before the

signals can be treated in this form, they must often first be synchronized and brought

to a common time base.

5.3.1.1 Simplification, Interpolation and Averaging of signals

The samples of signals available for analysis cannot always be processed directly. E.g.,

there are too many or too few samples corresponding to the sampling frequency for a

certain algorithm to be applied, or in the method to be applied, the sampling frequency

must be changed, as is the case, for example, with the discrete wavelet transform (see

subsubsection 5.3.3.2).

In the case of stochastic signals, it is often not the smaller random fluctuations

in the signal waveform, but rather the mean value that changes with time, which is

provided by a moving average (MA) filter in a given time interval before processing.

Changing the sampling frequency can be done in Matlab with the resample() com-

mand. However, this can also be done by omitting or adding samples followed by

low-pass filtering, which will be shown in the following sections.

Changing the Sampling Frequency

To change the sampling frequency, two cases must be distinguished in principle:

Either the sampling frequency must be decreased or increased.

1.

If the sampling frequency is to be decreased, the upper cutoff frequency of the

signal must not be greater than half the sampling frequency because of the neces-

sary compliance with the sampling theorem Equation 5.7. If, for example, every

second sample is omitted to reduce the sampling rate, the sampling frequency is

halved, but the maximum permissible cutoff frequency of the signal is also halved,

because of the sampling theorem. Before omitting samples, it must therefore be

checked whether the sampling theorem is still observed, and if not, the cutoff fre-

quency must be reduced with a low-pass filter (see Figure 5.8).