Chebyshev Filters

What are Chebyshev Filters?

Chebyshev filters are recursive low-pass filters borrowed from classical signal processing, named after mathematician Pafnuty Chebyshev, whose polynomials shape their frequency response. Applied to price, they do what every digital smoother does: pass the slow trend component and attenuate fast fluctuations. Their distinguishing property is the roll-off. For a given filter order, a Chebyshev design separates trend from noise more sharply than gentler designs such as the Gaussian Filter, at the cost of ripple, a small unevenness in how frequencies are passed or rejected.

The two standard types split by where that ripple lives. Type I allows ripple in the passband (the trend frequencies it keeps) in exchange for the steepest roll-off available from an all-pole filter of its order; Type II, the inverse design, keeps the passband flat and pushes the ripple into the stopband it rejects. On a chart, the practical consequences are aggressive noise rejection for the lag incurred, plus a tendency to overshoot slightly around sharp turns. Traders comparing filters usually weigh it against smoother, gentler designs like the Ehlers SuperSmoother.

How traders use it

• As a trend baseline: plot the filter on price and read slope and side, exactly as a moving average is used, but with a sharper split between what is smoothed away and what is kept.
• As a preprocessing stage: smooth price or an oscillator's input before computing signals, so crossovers and divergence reads fire on cleaned data rather than raw noise.
• As one half of a two-filter crossover: a fast and a slow Chebyshev filter (or a Chebyshev against a conventional average) crossing to time trend changes.