signal op• Data kinds: signal × indices → measurement
• Call: import fullseye as fs; fs.ledger.peak_subbin(x, idx=None, mode='parabola') (to call the implementation directly, import dsp; dsp.peak_subbin(x, idx=None, mode='parabola'); from the registry, ops1d.get("peak_subbin"))
Peak position between samples — the vertex of a fit through 3 points.
:func:find_peaks returns integer indices, so the position of a spectral
line or a correlation peak is quantised to the bin grid no matter how
finely the peak itself is resolved. This refines each index to a float by
fitting the sample and its two neighbours.
*mode* picks what is fitted:
`"parabola"`
`a x^2 + b x + c` through the three raw values. The classic estimator;
exact for a genuinely parabolic top and cheap.
`"gauss"`
the same parabola through `log` of the three values, which is exact for
a Gaussian peak. Requires all three values positive — a magnitude
spectrum qualifies, a signed correlation does not. Non-positive
neighbourhoods raise `ValueError` rather than silently returning the
integer index, because "the refinement quietly did nothing" is the
failure this operator exists to remove.
Measured on a Gaussian of width 1.7 bins centred at 40.37: the integer
argmax gives 40 (error 0.37 bins), `parabola` gives 40.3553 (error
0.0147) and `gauss` gives 40.3700 (error 0, to machine precision).
**The parabola is biased on a Gaussian, and the bias grows as the peak gets
narrower** — the same measurement at widths 6.0 / 3.0 / 1.7 / 1.0 bins errs
by 0.0012 / 0.0047 / 0.0147 / 0.0434. That is the whole reason `gauss`
exists: for a spectral line the log-parabola is not an approximation, it is
the exact model.
The refinement is still an assumption about shape, not a measurement of it.
On a triangular peak, whose top is not smooth, `parabola` errs by 0.0857
bins where the integer index errs by 0.30 — better, but three times worse
than on the Gaussian it was designed for.
The shift is not clamped. A vertex more than half a sample away from the
index means the index was not a local maximum in the first place, and that is
information: clamping it to +/-0.5 would return a plausible number for a bin
that has no peak in it. Run :func:find_peaks first, or clamp deliberately
at the call site when evaluating bins that are not maxima (a harmonic comb,
for instance).
A peak sitting on the first or last sample has no neighbour on one side and
keeps its integer position (there is nothing to interpolate against); the
returned array says so by being exactly equal to the input index there.
Parameters
----------
x : array_like
The 1-D signal the peaks were found in.
idx : int, sequence of int, or None
Peak indices. `None means "the argmax", so peak_subbin(mag)` is the
one-liner for a single line.
mode : {"parabola", "gauss"}
Returns
-------
float or ndarray
Refined position(s) in samples. Scalar in, scalar out.
See also
--------
find_peaks : which indices to refine.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_multibeam_bathymetry — py -3.11 examples/poc_multibeam_bathymetry.py
• poc_print_registration — py -3.11 examples/poc_print_registration.py
• poc_web_roll_periodicity — py -3.11 examples/poc_web_roll_periodicity.py
measurement as input)—
signal)lowpass · highpass · bandpass · envelope · rms · local_std · quantize · companding_mu_law
*Provenance: dsp.py — ONED operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.