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Swiss Army Knife - High-Pass Filter (SWAK_HP)

Summary

The high-pass row of John Ehlers' Swiss Army Knife filter: a one-pole detrender that removes what is slower than the cutoff period and keeps what is faster.

Read it as an oscillator, not as price. Its DC gain is 0, so a flat market returns zero and a trending one returns the trend's departure from itself rather than its level. That is the point of a detrender: what remains is the cyclic part of the series, centred on zero, which can then be measured or compared across instruments whose price levels differ by orders of magnitude.

The alpha is the cutoff-period one. Ehlers notes that it "is computed exactly the same as it is for the EMA", meaning the same construction, not TA_EMA's 2/(n+1).

Formula

w   = 2 * pi / optInTimePeriod
a1p = (cos(w) + sin(w) - 1) / cos(w)

c0  = 1 - a1p / 2
a1  = 1 - a1p

y[i] = c0 * (x[i] - x[i-1]) + a1 * y[i-1]

The filter is seeded in the steady state of a constant input equal to its first bar: the input slot starts at that bar and the output slot at zero, which is what a gain-0 row answers for a constant.

Notes

The period range starts at 5 because of arithmetic rather than taste. At a period of 4, cos(w) is 6.1e-17 and the numerator cos(w) + sin(w) - 1 rounds to exactly zero in doubles, so a1p is 0, both c0 and a1 become 1, and the filter degenerates into the integrator x[i] - x[s]. At a period of 2, cos(w) is -1 and c0 is 0, a filter that answers nothing at all. No contiguous range below 5 avoids both.

Every term of the recurrence exists at the first bar, so there is no structural lookback. What the first bars carry is the seed, which decays rather than ending: set TA_FUNC_UNST_SWAK_HP to discard bars until that transient is below whatever matters for the caller.

The output may alias the input. This row reads x[i-1], which an aliased write would already have overwritten, so it is carried in a local and never re-read from the input array.

Inputs

  • inReal — The series to detrend; Ehlers' default is the bar midpoint (H+L)/2, which the caller passes as TA_MEDPRICE output

Outputs

  • outReal — The detrended line, centred on zero

Parameters

ParameterTypeDefaultAccepted valuesDescription
optInTimePeriodinteger205–100000Cutoff period; cycles longer than it are removed, cycles shorter pass

Properties

Numerical Stability: Initial Unstable Period

☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1
☐ Display Shift

Implementation

TA-Lib Definition: swak_hp.c · swak_hp.yaml

NativeFile
Cta_SWAK_HP.c
Rustswak_hp.rs
JavaCore_SWAK_HP.java
C#Core_SWAK_HP.cs

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Swiss Army Knife High-Pass Filter, SWAK HP, Ehlers High-Pass Filter

See Also

SWAK_2PHP · SWAK_BP · MEDPRICE

References

  • Ehlers, John F. "Swiss Army Knife Indicator." Technical Analysis of Stocks & Commodities V.24:1 (January 2006), pp. 28-31, 50-53.
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