Filtered Ehlers Ultimate Smoother
The UltimateSmoother effectively retains low-frequency fluctuations in the input time series while diminishing high-frequency variations and noise.
The key input parameter for the Ultimate Smoother is the critical period, which denotes the minimum wavelength (highest frequency) within the filter's pass band. In simpler terms, the filter reduces or eliminates the amplitudes of oscillations that occur at shorter periods than the critical period.
As noted by Ehlers, a significant benefit of the Ultimate Smoother is its ability to maintain zero lag in its pass band and minimal lag in its transition band, setting it apart from traditional digital filters (such as moving averages). This smoother can be utilized on a variety of input data series, including other indicators.
Calculation
Ehlers developed the Ultimate Smoother by drawing inspiration from the design principles he acquired through his experience with analog filters, as outlined in the original publication.
On a technical level, the distinctive response of the Ultimate Smoother consists of subtracting a high-pass response from an all-pass response.
At extremely low frequencies (long periods), where the high-pass filter response exhibits nearly no amplitude, the subtraction results in a frequency and phase response that is almost identical to the input data.
At other frequencies, the subtraction facilitates filtration through cancellation, owing to the close similarities in response between the high-pass filter and the input data.
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