5 Methods for Discrete Processing and Analysis of

Biosignals

5.1 Discretisation of Continuous Signals

After the analogue measurement of the biosignal, amplification and, if necessary, fil-

tering, it is sampled with pulses at discrete points in time (pulse modulation), and only

these measured values are used for further processing. If a time-continuous signal is

to be generated again after the discrete-time processing, interpolation must be car-

ried out between the discrete-time values. The way in which this interpolation takes

place can best be examined in the spectral range. For this purpose, the spectra before

and after the sampling as well as after the interpolation system are considered. The

interpolation is done by low-pass filtering.

After the interpolation, the original continuous-time signal must arise again (see

Figure 5.1). For this purpose, an equivalent system is considered in which the switch

for sampling is replaced by a multiplier that multiplies the input signal with a square-

wave pulse train (cf. Figure 5.2).

The multiplication with a square-wave pulse train can also be replaced by a multi-

plication with a Dirac-pulse train, whereby after the multiplication the now resulting

weighted Dirac-pulse train fTa(t) is still changed back into a square-wave pulse train

by a pulse shaper (see Figure 5.3). This is because it does not matter whether the input

signal is multiplied by a square-wave pulse train or a Dirac-pulse train before the mul-

tiplication, whereby the square-wave formation takes place after the multiplication.

The output signal f∆T after sampling and pulse shaping is obtained by convolution

of the signal sampled with Dirac pulses.

fTa(t) =

∞

∑

k=−∞

f(kTa) ⋅δ(t −kTa)

(5.1)

with the impulse response

Fig. 5.1: Uniform sampling of a signal in the ta = nTa, n = 1, 2, . . . with sampling interval Ta and

subsequent interpolation using low-pass filtering.

https://doi.org/10.1515/9783110736298-005