Smoothing & filters

Track and denoise the level of a series: moving averages and designed filters.

Smoothing & moving averages

Track the level of a series and suppress short-term noise.

Function	Description
Butterworth low-pass filter	General-order IIR Butterworth low-pass filter.
Double Exponential MA (DEMA)	Mulloy's Double EMA: 2*EMA - EMA(EMA).
Exponentially-weighted mean	Exponentially-weighted moving average (pandas adjust=True).
Hull MA	Hull's responsive MA: WMA(2*WMA(n/2) - WMA(n), sqrt(n)).
Scalar Kalman filter	Scalar 1-D Kalman filter for a noisy random-walk model.
Kaufman Adaptive MA (KAMA)	Adaptive MA whose smoothing constant responds to the efficiency ratio.
FIR moving average (arbitrary taps)	Finite-impulse-response filter with user-supplied taps.
Rolling mean	Trailing-window arithmetic mean (simple moving average).
Rolling 2nd-order polynomial fit	OLS fit y = a + b*t + c*t^2 over a trailing window.
Triple Exponential MA (TEMA)	Mulloy's Triple EMA: 3*EMA - 3*EMA(EMA) + EMA(EMA(EMA)).
Triangular MA (TRIMA)	Triangular MA: SMA of an SMA. Heavier center-weighting than WMA.
Weighted Moving Average (WMA)	Linearly-weighted moving average. O(1) per step.

Filtering

Designed frequency-domain and state-space filters.

Function	Description
Butterworth low-pass filter	General-order IIR Butterworth low-pass filter.
Butterworth band-pass filter	General-order IIR Butterworth band-pass filter.
Butterworth band-stop filter	General-order IIR Butterworth band-stop (notch) filter.
Butterworth high-pass filter	General-order IIR Butterworth high-pass filter (rejects low frequencies).
Hampel filter	Robust Hampel despiker, replace samples far from the window median (in MAD units).
Scalar Kalman filter	Scalar 1-D Kalman filter for a noisy random-walk model.
FIR moving average (arbitrary taps)	Finite-impulse-response filter with user-supplied taps.
Schmitt trigger (hysteresis comparator)	Hysteresis comparator. Latches 1.0 above the upper threshold, 0.0 below the lower threshold, and retains its previous value in between.