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6 Applications and Methods in Biosignal Processing

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

f / Hz

0

10

20

30

40

50

60

70

80

PSD (normalized)

Fig. 6.36: Associated power spectral density according to Lomb created with HRVAS, see [44].

but often only a three-day ECG is obtained. In order to still obtain accurate measure-

ments, the windows can be adjusted (e.g. according to Gauss, Hanning, Han, Kaiser,

etc.) so that no major errors occur in the frequency range, e.g. due to overshoots.

The discrete-time short-time-Fourier transformation is defined by the relation

X(m, ω) =

∞

∑

b=−∞

x(n) ⋅w(n −m)e^−jωn

(6.29)

Here x(n) is the sampled signal (here the ECG), and X(m, ω) is the sliding window

defined by the window function w(n−m) whose position is described by m. This spec-

trum is not discrete, as in the case of the discrete-time Fourier transform. Only when

the input signal is periodic does the discrete-time Fourier transform change to the dis-

crete one. Since the heart beats rhythmically, the periodicity is virtually assumed in

the recording. However, since the heart does not beat purely periodically, but varies,

errors occur in the determination of the spectrum.

In order to improve the spectral resolution, wavelet transformations can be used,

which have a shorter window at higher frequencies, i.e. at lower frequencies one has a

poor spatial resolution with good frequency resolution, while in the higher frequency

range it is exactly the opposite (cf. section 2.4).

6.3.2 Phonocardiogram

In section 4.3 the technique of registration of heart tones was presented. Figure 6.37

(top) shows a phonocardiogram of 20 s duration. In it, the two heart sounds are rhyth-

mically repeated.

The first heart sound is produced by the contraction of the ventricles and is also

called the force sound. Under physical stress, the amplitude of the first heart sound

increases, because the increased oxygen demand of the organism causes a greater