4.5 Design of Analogue Filters

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123

8th order

2nd order

12th order

Fig. 4.32: Frequency response of group delay times for 2nd, 8th and 12th order Bessel filters.

4.5 Design of Analogue Filters

Electrical filters are often used in the signal processing of biological measurands to:

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suppress interfering signals such as mains hum, noise, measurement errors or

errors caused by transducers when the patient moves,

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select desired useful signals, e.g. in ECG,

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improve detectability, e.g. by applying the raised-cosine filter in the transmission

of digital signals,

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limit the highest frequency of the signal spectrum, so that when the conditions for

sampling (sampling theorem) when the signal is later sampling conditions (Shan-

non sampling theorem) are met, and to

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improve the ratio between useful and interfering signal power for later processing

(interference ratio increase e.g. by matched- or Kalman-Filter).

Analogue filters can be realised either by purely passive components such as resistors,

coils and capacitors or in combination with active components that increase the signal

energy, such as transistors or operational amplifiers.

For the application in the biological field, two important design goals will be de-

scribed in more detail below: i) the design of selective analogue filters to optimise the

magnitude frequency response and ii) the design of analogue filters with linear phase

response to achieve a constant progression of the group delay, which is particularly

important, for example, for the analysis of an ECG.

4.5.1 Selective Filters to Optimise the Magnitude Frequency Response

Selective filters filter out a part of a signal spectrum. In this way, for example, the spec-

trum of the useful signal can be limited in order to digitise it afterwards (antialiasing-