Swiss Army Knife - Band-Pass Filter (SWAK_BP)

Summary

The band-pass row of John Ehlers' Swiss Army Knife filter: a cycle extractor that keeps a band of periods around a chosen centre and removes everything on both sides of it.

Read it as an oscillator, not as price. It answers zero on a constant, zero on a bar-to-bar alternation, and exactly the input, with the same amplitude and no phase shift, on a sine wave at the centre period. Between those it tapers, with the half-power points near P(1 ± delta): at a centre of 20 bars and a delta of 0.1 the band is roughly 20 ± 2 bars.

What separates it from the high-pass rows is that it rejects the fast end too. A detrender keeps everything above its cutoff, including the bar-to-bar noise; this keeps only the band asked for.

Formula

w    = 2 * pi / optInTimePeriod
beta = cos(w)
t    = 4 * pi * optInDelta / optInTimePeriod
abp  = (1 - sin(t)) / cos(t)

c0   = (1 - abp) / 2
a1   = beta * (1 + abp)
a2   = -abp

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

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, since a band-pass of a constant is zero.

Notes

abp is written as (1 - sin t) / cos t rather than the published gamma - sqrt(gamma^2 - 1) with gamma = 1 / cos t. The two are equal for 0 < t < pi/2, which this function's ranges guarantee, but the published form loses precision as t approaches zero because gamma^2 - 1 goes as t^2. Measured against a 60-digit reference, the published form is already 4.5e-13 off at the period cap, which is what would otherwise force a lower cap.

The period range starts at 5 so that delta <= 0.5 keeps t below pi/2, where both forms agree and abp stays in (0, 1). Below that the published form can return a value that makes the recurrence unstable.

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_BP to discard bars until that transient is below whatever matters for the caller. This row settles more slowly than the others at the same period: its poles sit near the unit circle, which is what makes the band narrow.

The output may alias the input. This row reads x[i-2], which an aliased write would already have overwritten, so the input slots are carried in locals and never re-read from the input array.

Inputs

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

Outputs

outReal — The extracted cycle, centred on zero

Parameters

Parameter	Type	Default	Accepted values	Description
`optInTimePeriod`	integer	20	5–2000	Centre period of the band; the filter passes this one untouched
`optInDelta`	real	0.1	0.05–0.5	Half-bandwidth as a fraction of the centre period; smaller is a narrower band and a longer settling transient

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_bp.c · swak_bp.yaml

Native	File
C	`ta_SWAK_BP.c`
Rust	`swak_bp.rs`
Java	`Core_SWAK_BP.java`
C#	`Core_SWAK_BP.cs`

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

Aliases

Swiss Army Knife Band-Pass Filter, SWAK BP, Ehlers Band-Pass Filter

References

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