Chebyshev filter

Chebyshev filters, named in honor of Pafnuty Chebyshev, are analog or digital filters of a kind related to Butterworth filters, but having a steeper roll-off, but more passband ripple. They have the property that they minimise the error between the idealised filter characteristic and the actual over the range of the filter, but as noted, there can be ripples in the passband. For this reason filters which have a smoother response in the passband but a more irregular response in the rejection bands are preferred for some applications.