170

|

5 Methods for Discrete Processing and Analysis of Biosignals

discrete time n

shift j

heart rate / min-1

Fig. 5.14: Matlab-Representation of a human heart rate (top) with associated auto-covariance (bot-

tom) using the supplementary material to [6].

Fig. 5.15: Unit-pulse δ(n).

Here, a normally distributed mean-free random number sequence with 5000 values

was generated with Matlab using the function randn() and then its auto-covariance

was calculated with xcov() and normalised to a maximum value of one. You can see

very clearly that this produces the function of a unit impulse (see Figure 5.15), which

is approximated the better the more values the random number sequence has.

Another example shows Figure 5.14. Here the auto-covariance of the heart rate of

a human is shown. The similarity to white noise disappears and one can see a periodic

progression. This can be explained, for example, by the influence of periodic breath-

ing, which also changes the heart rate periodically.