Chebyshev filters have the following characteristics:
- Minimization of peak error in the passband
- Equiripple magnitude response in the passband
- Monotonically decreasing magnitude response in the stopband
- Sharper roll-off than Butterworth filters
Compared to a Butterworth filter, a Chebyshev filter can achieve a sharper transition between the passband and the stopband with a lower order filter. The sharp transition between the passband and the stopband of a Chebyshev filter produces smaller absolute errors and faster execution speeds than a Butterworth filter.
The following figure shows the frequency response of a lowpass Chebyshev filter.
In the previous figure, the maximum tolerable error constrains the equiripple response in the passband. Also, the sharp roll-off appears in the stopband.