HighpassFilter

Ehlers' two-pole highpass filter — strips the low-frequency trend and leaves the cyclic content; the complement of the Decycler.

Quick reference

Field	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64
Output range	zero-mean (price units)
Default parameters	(period = 48) (Python)
Warmup period	1
Interpretation	Detrended series — swings around 0 with the cycles.

Formula

a = 0.707 · 2π / period
alpha1 = (cos(a) + sin(a) − 1) / cos(a)
HP_t = (1 − alpha1/2)² · (price_t − 2·price_{t−1} + price_{t−2})
       + 2·(1 − alpha1)·HP_{t−1} − (1 − alpha1)²·HP_{t−2}

The two-pole highpass passes everything faster than the cutoff period and removes the slow trend, detrending the series into a zero-mean wave with a steep roll-off. It is the part the Decycler discards: decycler = price − highpass. Source: crates/wickra-core/src/indicators/highpass_filter.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	48 (Python)	>= 1	highpass_filter.rs:55	Cutoff period; cycles slower than this are removed. 0 errors with Error::PeriodZero.

The period getter returns the cutoff; value returns the current output if ready.

Inputs / Outputs

From crates/wickra-core/src/indicators/highpass_filter.rs:

use wickra::{Indicator, HighpassFilter};
// HighpassFilter: Input = f64, Output = f64
const _: fn(&mut HighpassFilter, f64) -> Option<f64> = <HighpassFilter as Indicator>::update;

An f64 in, an Option<f64> out. The Python binding takes a scalar for update and a 1-D numpy array for batch; Node takes update(value) and batch(values[]). With warmup_period == 1 a value is produced every bar (zeros until the recursion fills).

Warmup

warmup_period() == 1. The first two bars emit 0, then the filter is live (first_bars_are_zero pins this).

Edge cases

• Flat input → 0. A constant has no high-frequency content (constant_input_stays_zero pins this).
• Pure trend → attenuated. A straight ramp is low-frequency and is driven small after warmup (pure_trend_is_attenuated pins this).
• Non-finite input. A NaN/∞ input is ignored and the last value returned (ignores_non_finite pins this).
• Reset. hp.reset() clears the price/output history and the last value (reset_clears_state).

Examples

Rust

use wickra::{BatchExt, Indicator, HighpassFilter};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut hp = HighpassFilter::new(20)?;
    // A ramp + ripple: the ramp is removed, the ripple survives.
    let xs: Vec<f64> = (0..200).map(|i| 100.0 + f64::from(i) + (f64::from(i) * 0.5).sin() * 3.0).collect();
    println!("last = {:?}", hp.batch(&xs).last().unwrap());
    Ok(())
}

Python

import numpy as np
import wickra as ta

hp = ta.HighpassFilter(48)
x = 100 + np.arange(200) + np.sin(np.arange(200) * 0.5) * 3
print(hp.batch(x)[-5:])  # detrended ripple

Node

const ta = require('wickra');

const hp = new ta.HighpassFilter(48);
console.log('warmupPeriod:', hp.warmupPeriod()); // 1

Streaming

use wickra::{Indicator, HighpassFilter};

let mut hp = HighpassFilter::new(48).unwrap();
let mut last = None;
for i in 0..120 {
    last = hp.update(100.0 + f64::from(i) + (f64::from(i) * 0.5).sin() * 3.0);
}
println!("{last:?}");

Streaming update and batch are equivalent tick-for-tick (batch_equals_streaming pins this).

Interpretation

1. Detrending. Feed any indicator the highpass output to remove slow drift before measuring cycles.
2. Roofing front-end. Pair with a SuperSmoother lowpass to build a roofing filter (highpass then smooth) — the basis of much of Ehlers' work.
3. Cycle visibility. Turning points in the highpass mark short-cycle swings that the raw chart buries under the trend.

Common pitfalls

• Not the decycler. This is the cycle part; for the smoothed trend use the decycler (price − highpass).
• Cutoff choice. Too long a period lets slow swings leak through; too short removes genuine cycles.
• Zero-mean. The output centres on 0, not on price.

References

Ehlers, J. F. (2013), Cycle Analytics for Traders, Wiley — the two-pole highpass and roofing filter.

See also

• Indicator-Decycler — the trend complement (price − highpass).
• Indicator-BandpassFilter — single-band cycle isolator.
• Indicator-RoofingFilter — highpass + SuperSmoother.
• Indicators-Overview — the full taxonomy.