Application
Smoothing signals with low-pass filters
The ability of low-pass filters to attenuate high frequencies is used to smooth signal profiles. The following diagram shows the step response of low-pass filters of different orders, but with the same cut-off frequency of 1Hz.
It is found that the maximum slope of the step response is almost independent of the filter order. It can therefore be estimated on the basis of the slope at the start of the step response of a filter of the 1st order, which is easy to calculate.
For a step ∆x at the input of a low-pass filter with the cut-off frequency fg, we arrive at the following equation 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.
