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Swiss Army Knife - Two-Pole High-Pass Filter (SWAK_2PHP)

Summary

The two-pole high-pass row of John Ehlers' Swiss Army Knife filter: the same double real pole the Gaussian and Butterworth rows use, with a detrending numerator instead of a smoothing one. It removes what is slower than the cutoff period and rolls off twice as steeply as the one-pole row.

Read it as an oscillator, not as price. Its DC gain is 0, so a flat market returns zero and a trend returns its departure from itself. Against TA_SWAK_HP the difference is the slope of the transition: the second pole buys a sharper separation between what is kept and what is removed.

Formula

w   = 2 * pi / optInTimePeriod
b2p = 2.415 * (1 - cos(w))
a2p = -b2p + sqrt(b2p^2 + 2 * b2p)

c0  = (1 - a2p / 2)^2
a1  = 2 * (1 - a2p)
a2  = -(1 - a2p)^2

y[i] = c0 * (x[i] - 2 * x[i-1] + x[i-2]) + a1 * y[i-1] + a2 * y[i-2]

The numerator is zero on a constant, which is what makes the DC gain 0. At Nyquist it weighs 4, and c0 divides that back to exactly 1.

The filter is seeded in the steady state of a constant input equal to its first bar: both input slots start at that bar and both output slots at zero.

Notes

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_2PHP to discard bars until that transient is below whatever matters for the caller. The pole is a repeated real root, so the transient decays as k * (1 - a2p)^k rather than as a plain geometric.

The output may alias the input. This row reads x[i-1] and x[i-2], which an aliased write would already have overwritten, so both are carried in locals 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
optInTimePeriodinteger202–10000Cutoff 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_2php.c · swak_2php.yaml

NativeFile
Cta_SWAK_2PHP.c
Rustswak_2php.rs
JavaCore_SWAK_2PHP.java
C#Core_SWAK_2PHP.cs

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

Aliases

Swiss Army Knife Two-Pole High-Pass Filter, SWAK 2PHP, Ehlers Two-Pole High-Pass Filter

See Also

SWAK_HP · 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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