252

|

6 Applications and Methods in Biosignal Processing

Fig. 6.25: Amount frequency response of the differentiator |ADif(ωT)| according to Figure 6.22.

on the window position of the n-th sample in which the N = 30 samples are located.

The algorithm is

yMA(n) = [xMA(n) + xMA(n −1) + ⋅⋅⋅+ xMA(n −(N −1))]/N .

In the time domain, we then obtain for the transfer function AMA(z):

AMA(z) = ^YMA(z)

XMA(z) ^{= 1}

N

N−1

∑

i=0

z^{−^ı} = ¹

N

1 −z^−N

1 −z^{−1 ,}

geometcic series

(6.23)

and thus for the magnitude frequency response (cf. Figure 6.26):

|AMA(ωT)| =

󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨

1

N ^z−N−1

2 ⋅^{sin( N}

2 ^ωT)

sin(ωT/2)

󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨

= ¹

N

󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨

sin( ^N

2 ^ωT)

sin(ωT/2)

󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨

.

(6.24)

From the transfer function in Equation 6.24, we see that the window integrator has a

signal delay of (N−1)/2 samples. With a window width of 30 samples this corresponds

to (30 −1)/2 ⋅5 ms = 72.5 ms.

In the subsequent investigation of whether a QRS complex is present, it must be

noted that the ECG signal at the output of the sliding window integrator is delayed

compared to the original ECG (see Figure 6.28). The delay results from the 25 ms for the

low-pass, the 80 ms for the high-pass, the 10 ms for the differentiator and the 72.5 ms

for the window integrator at a sampling frequency of 200 Hz. The total delay time is

therefore 25 ms + 80 ms + 10 ms + 72.5 ms ≈190 ms and must be considered when

determining the location of the QRS complex.

This can also be seen in the example shown in Figure 6.27, where for an ECG dis-

turbed by noise, the signals at the output of each processing block are shown.

Searching the QRS Complex

After integrating 30 samples through the sliding window, the search for the QRS com-

plex begins both in the output signal after window integration and in the ECG signal