Butterworth filters have the following characteristics:
- Smooth response at all frequencies
- Monotonic decrease from the specified cut-off frequencies
- Maximal flatness, with the ideal response of unity in the passband and zero in the stopband
- Half-power frequency, or 3 dB down frequency, that corresponds to the specified cut-off frequencies
The advantage of Butterworth filters is their smooth, monotonically decreasing frequency response. The following figure shows the frequency response of a lowpass Butterworth filter.
As shown in the previous figure, after you specify the cut-off frequency of a Butterworth filter, the steepness of the transition is proportional to the filter order. Higher order Butterworth filters approach the ideal lowpass filter response.
Butterworth filters do not always provide a good approximation of the ideal filter response because of the slow roll-off between the passband and the stopband.