Chebyshev filter

The Chebyshev filter is a family of signal processing filters that achieve a steeper roll-off than the Butterworth filter by permitting a controlled amount of ripple in either the passband (Type I) or the stopband (Type II). Named after the Russian mathematician Pafnuty Chebyshev, whose polynomials govern the filter's frequency response, it represents a design philosophy that accepts controlled imperfection in exchange for superior selectivity.

The Chebyshev filter is the engineer's admission that the ideal filter is unattainable, and that the best design is the one that makes the right trade-off between conflicting errors. The Elliptic filter goes further, permitting ripple in both passband and stopband to achieve the sharpest possible transition.