Low-pass filters

Frequency response

The diagram below shows the frequency transmission response of low-pass filters that are each based on one of the filter prototypes. To elucidate the characteristic transmission response, filters of the 4th order were chosen because the characteristics are more distinct due to the higher order.

In the range below the cut-off frequency, low-pass filters of the "critical attenuation" and "Bessel" prototypes have very similar responses. In this range, Butterworth filters transmit almost without attenuation over a wide range. Attenuation of the transmitted frequencies only sets in just before the cut-off frequency. Of the filters presented here, the Butterworth filter has the highest attenuation in the range above the cut-off frequency.

Step response

The step response of a low-pass filter with "critical attenuation" does not display any overshoot. This is why this filter is highly suitable for control applications despite its lower frequency selection response compared to other filters.

A slight overshoot with filter orders > 1 can be observed in the case of Bessel low-pass filters. This is why this filter should not be applied to position values.

In the case of Butterworth low-pass filters considerable overshoot is exhibited in response to an abrupt change at the input. The overshoot increases with the filter's order. Due to this keen reaction, the Butterworth low-pass filter is unsuitable for control applications.

Example

Axis filters 4th order low-pass filters with a cut-off frequency of 15 Hz:

Example

Additional interface: 3rd order low-pass filters with a cut-off frequency of 8 Hz: