6.3 Signals of the Cardiovascular System

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251

Fig. 6.24: Amount frequency response |AHP(f)| for the high-pass component of the bandpass accord-

ing to Figure 6.22.

so that only samples that lie in the past can be taken. The associated filter algorithm

will therefore produce a delayed differentiation:

yDif(n) = ̃yDif(n −2) = (2xDif(n) + xDif(n −1) −xDif(n −3) −2xDif(n −4))/8 .

(6.19)

The transfer function ADif(z) is then obtained according to

ADif(z) = ^YDif(z)

XDif(z) ^{= 1}

8^{(2 + z−1 −z−3 −2z−4)}

(6.20)

with the associated magnitude frequency response represented in Figure 6.25 in

double logarithmic measure.

|ADif(ωTa)| = ¹

4^{[2 sin(2 ωTa) + sin(ωTa)] .}

(6.21)

From the double logarithmic plot, it can be seen that the differentiator is up to approx-

imately 30 Hz the magnitude frequency response rises linearly and then drops steeply.

Up to approximately 30 Hz, however, most spectral ranges are contained. The drop

thereafter causes an additional attenuation of higher-frequency interference compon-

ents (e.g. 50-Hz-mains hum).

Square

This non-linear limb causes additional amplification of the QRS complex highlighted

by the differentiator according to the simple instruction

yquad(n) = x²

quad^{(n) ,}

xquad, yquad : input and output of the squarer

(6.22)

Window Integration (MA – Moving Average)

In the subsequent moving-window-integration, 30 samples (corresponding to 30 ⋅

5 ms = 150 ms) are averaged in a time interval and continuously output depending