This example is a continuation of the first example on sampling.
Butterworth filters constitute a family of filters which share certain characteristics.
We will consider only low-pass Butterworth filters in this example. The result is that at the cutoff frequency, the filter's magnitude is -3 db, regardless of the order of the filter. Bode plots for the magnitudes and phases of Butterworth filters for orders 1-4 are shown below. Magnitude Curves Butterworth Filter Phase Curves Note that the higher the order of the filter, the steeper the roll-off in the magnitude is. This means that there can be a narrower band of frequencies between those which are passed by the filter and those which are rejected.