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5 Methods for Discrete Processing and Analysis of Biosignals

FIR-LP

Sampling points

ideal LP

Fig. 5.47: FIR low-pass 15 order according to Figure 5.45 where the sample at the filter edge at

200 Hz has been lowered to 0.4.

In general, however, the measured biosignals are not periodic and therefore do not

have a discrete frequency spectrum. If the FIR filter just designed is now applied to

these signals, an error occurs. To estimate this, the impulse response is determined. In

this case, the transfer function of the FIR filter is no longer discrete, but continuous in

frequency. In Figure 5.45 it can be seen that between the given values of the magnitude

frequency response very large deviations from the ideal lowpass can occur, which are

called overshoots.

This can be remedied by no longer attempting to sample the ideal lowpass, which

has a very large slope, but by replacing the steep slope with a smoother transition from

the passband to the stopband. As an example of this, the sample point with the value

1 at the edge at 200 Hz is to be replaced by a value of 0.4. The result shows Figure 5.47.

It can be clearly seen that the flatter edge at 200 Hz greatly reduced the overshoots in

the frequency response compared to the steep edge according to Figure 5.45.

5.4 Post-Reading and Exercises

Discretisation

1.

Explain the process of discretisation and quantisation in the context of analogue-

digital-conversion of signals.

2.

Explain the Shannon theorem.

3.

What effect of analogue to digital conversion is called aliasing?

4.

Explain the effect of an anti-aliasing filter.

5.

What is the purpose of a sample-and-hold amplifier before an analogue-to-digital

converter?