Butterworth filter

The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. First described by British engineer Stephen Butterworth in 1930, it is the maximally flat approximation to the ideal low-pass filter: it has no ripple in the passband and a monotonic roll-off in the stopband. The trade-off for this flatness is a gradual transition from passband to stopband compared to other filter families like the Chebyshev filter or the Elliptic filter.

The Butterworth filter represents a conservative design philosophy: it prioritizes the preservation of signal integrity within the passband over the sharpness of frequency selectivity. This makes it the default choice for applications where passband distortion is more costly than stopband leakage, such as audio crossover networks and anti-aliasing filters.