6.3 Signals of the Cardiovascular System

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263

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

f / Hz

0

0.005

0.01

0.015

PSD (s2/Hz)

Fig. 6.35: With HRVAS created associated power spectral density according to Welch, see [81] .

give better results. With the wavelet transform the signal need not be stationary and

with Lomb’s method [44] need not be uniformly sampled.

In the method of Lomb [44] the time intervals between the samples (interbeat

interval IBI) are determined by a sine function with delay according to

IBI(tn) + εn = a cos(2πf[tn −τ]) + b sin(2πf[tn −τ]) .

(6.28)

for all N values of the signal IBI(tn), n = 1, . . . , N at a given frequency f is approxim-

ated by varying the values of a,b and τ such that the error ε is smallest. A previous in-

terpolation and sampling in a uniform manner is not necessary here. As can be seen by

comparing the power spectral density according to the Welch and Lomb method, the

spectrum according to Welch is more bell-shaped than that according to Lamb, which

speaks for a more detailed resolution of the Lomb method. Both spectral power dens-

ities were created with the software tool HRVAS by Ramshur [66], which can not only

perform the spectral power densities but also analyses in the time and time-frequency

composite range. In addition, various preprocessings are possible, such as the sup-

pression of very low-frequency components (detrending) or artefacts caused, for ex-

ample, by patient movement with electrode displacements. The tool can be down-

loaded free of charge from the internet at https://github.com/jramshur/HRVAS and

can be installed either as an extension of Matlab and Scilab or without them as a stand-

alone package.

The autocorrelation serves for further spectral investigation. It can also be under-

stood as a convolution with its own mirrored course. By Fourier transforming the auto-

correlation of the heart rate according to Equation 6.27, its spectral power density can

be calculated and compared with the quadratic amount of the Fourier transform in

order to better estimate the actual spectrum. In practical recordings, only a section of

the actual ECG is available. Ideally, a long-term ECG of up to seven days would be used,