Every electronic filter is a compromise between flat, sharp and smooth
An ideal filter would let wanted frequencies through untouched and block everything else instantly. No real circuit can. Engineers instead pick a family, such as Butterworth, Chebyshev, Bessel or elliptic, each trading flatness, steepness or timing against the others by approximating perfection with a different polynomial.
In signal processing, a filter strips unwanted parts from a signal, suppressing some feature fully or partly. Usually that means cutting certain frequencies, though image processing and other fields filter for other targets too. Filters turn up almost everywhere electricity carries information: radio, television, radar, audio recording, music synthesisers, control systems, computer graphics, even the study of how structures vibrate.
There is no tidy family tree for them, because the ways of sorting overlap. A filter may be analogue or sampled, passive or active, and fixed or changing over time. Digital designs split into infinite and finite impulse response types. One distinction sounds almost paradoxical: a non-causal filter uses future input to compute its present output. That is impossible for live audio, but perfectly fine for a recording processed afterwards or for an image, where the data is all there at once.
In analogue electronics the word usually means a linear circuit. Linearity matters, since a nonlinear stage would invent frequencies absent from the input. Designers describe behaviour by which band passes and which is rejected. Low-pass circuits keep bass and cut treble; high-pass do the reverse; band-pass keep a slice; band-stop remove one; a notch knocks out a single frequency; a comb creates evenly spaced narrow windows; and an all-pass lets everything through while shifting phase. Key terms include cutoff frequency, often set where the signal falls by 3 dB, roll-off for how quickly attenuation grows beyond it, and ripple for unevenness in the passband.
Modern designs come from a method called network synthesis. Butterworth gives the flattest passband, Bessel the most even time delay, Chebyshev the closest overall match to the ideal for a given complexity and ripple, and elliptic the steepest cutoff. The order, meaning the degree of the polynomial and in passive circuits the number of components, sharpens the result as it rises. An older approach produced wave filters such as the constant k and its improved m-derived cousin.
Source: Filter (signal processing)
