4.4 Interference Suppression and Analog Filtering

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frequency. In any case, however, the biosignal spectrum lies within the noise spec-

trum. By means of a bandpass filter whose passband includes the biosignal spec-

trum, the noise power can be reduced linearly to the bandwidth of the filtered

component.

3.

Transient Interference: As already described in subsection 4.2.2, transient disturb-

ances can occur during power-on processes due to the charging of the capacitance

of the high-pass filter in the measurement amplifier. The charging curve is propor-

tional to −e^−t/τ, where τ is the time constant of the high-pass filter. With R = 1 MΩ

and C = 1 μF, the time constant is τ = 1 s. The spectrum of the charge function is

proportional to ^√1/(1 + ω²τ²). With the calculated time constant, the spectrum

of transient disturbances overlaps the lower frequency range of most biosignals.

4.

Pulse type disturbances: Causes can be artifacts or also pulse-like processes in

technical equipment, which couple into the measuring signal. The spectrum of

an ideal, infinitesimally narrow pulse is infinitely extended. In the case of a real

pulse with temporal expansion, the spectrum falls off towards high frequencies.

The simplest way to realize filters electronically is to use low-pass and high-pass cir-

cuits of RC elements. Bandpass and bandstop filters can be created by connecting low-

pass and highpass in series and parallel, respectively. The cutoff frequency can be set

by selecting the resistor and capacitance values. The cutoff frequency indicates the

frequency value at which the transfer function is dropped by 3 dB (corresponding to

the factor ¹/^√2) with respect to the passband. For a simple RC filter (first-order filter),

the cutoff frequency is:

fg =

1

2πRC ^.

(4.10)

The slope is20 dB/frequencydecade. If steeper edgesarerequired,thiscanbeachieved

byconnecting the same filter in series several times.Thentheslopeis n20 dB/frequency

decade, where n is the number of filters connected in series (filter order). However,

when connecting in series, it should be noted that this shifts the cutoff frequency. For

example, if two identical filters are connected in series, the cutoff frequency is a factor

of 0.37 smaller than the cutoff frequency of a single-stage filter, if the −3 dB- criterion

for the cutoff frequency continues to apply.

The calculation of the cutoff frequency in Equation 4.10 assumes that the internal

resistance of the signal source at the filter input is very small and the load at the fil-

ter output is very large, both related to the impedance of the RC circuit. If this is not

the case, internal resistance and load must be considered when calculating the trans-

fer function of the filter and the resulting cutoff frequency. If then still the impedance

values of the internal resistance and the load are not known or are known only inac-

curately, the filter characteristic, especially with regard to the cut-off frequency, can

no longer be controlled.

One way out is the use of operational amplifiers. These have a very high input res-

istance and a very low output resistance. This electrically decouples the filter output