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6 Applications and Methods in Biosignal Processing

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t / hh:mm:ss

0.92

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IBI / s

Fig. 6.34: Example of the time intervals between the R-waves of an ECG (IBI: Interbeat intervals) with

an average heart rate of 60 beats per minute, generated with the software tool ECGSYN, see [48].

Analysis in the Frequency Domain

When analysing in the frequency domain, it must be noted that the discrete values for

the heart rate in Equation 6.25 do not have equal intervals, but act like an irregular

sampling of a continuous heart rate course due to the different lengths of the RR in-

tervals, i.e. a Fourier transformation cannot be applied directly, as this presupposes

equal time intervals between the samples. In order to create this prerequisite, the heart

rate can first be converted into a time-continuous form by interpolation, which is then

digitised again by uniform sampling in order to be able to transform it into the fre-

quency domain (cf. Figure 6.34).

The simplest form of interpolation is to interpolate the irregular values of the

measured heart rate linearly or with spline functions. However, this increases the ra-

tio of the spectral components of the lower to those in the higher frequency range

[7]; because this interpolation can act like a low-pass filter. With linear interpolation,

this still does not receive a smooth (i.e. continuously differentiable) course, but many

corners, which lead to additional frequency components in the spectrum, which are

not present in the measured heart rate. With the interpolation by spline-functions,

this problem is reduced. A further reduction can be achieved by dividing the recor-

ded interval into several smaller intervals which overlap and are supplemented with

a weighting function (e.g. Hamming window), see [81]. The basis for these methods

is the Fourier transformation. The prerequisites for their application or models with

recursive feedbacks, in which the coefficients of the model are estimated (Autoregress-

ive (AR) models) presuppose that the signal is stationary and sampled uniformly. How-

ever, this is rarely the case in biological systems, so other methods, such as the wavelet

transform or spectral estimation using delay and least square error minimisation, can