# Application

## Smoothing signals with low-pass filters

The ability of low-pass filters to attenuate high frequencies is used to smooth signal profiles. The diagram below shows the step response of low-pass filters of different orders but with the same cut-off frequency of 1 Hz.

It is found that the maximum slope of the step response is almost independent of the filter order. As a result, it can be estimated from the slope at the start of the step response of a first-order filter. This requires only a simple calculation.

For a step ∆ x at the input of a low-pass filter at cut-off frequency f_{g} the following equation is obtained for the maximum slope of the output signal:

This equation is important because it reflects the relationship between the bandwidth of the signal and the maximum slope of the filtered signal.