order_spectrum — ACOUSTICS order op

Data kinds: signaltable

Call: import acoustics; acoustics.order_spectrum(x, rate, rpm, samples_per_rev=64, revolutions=None, max_order=None, n_peaks=5) (or opsacoustics.get("order_spectrum"))

Usage

Amplitude against shaft order — the spectrum a run-up should be read in.

:func:angular_resample followed by an rFFT over a **whole number of

revolutions** (the record is cropped to that). Bin spacing is

`1 / whole_revolutions` in orders.

`revolutions` overrides how many whole revolutions to keep, and it matters

more than it looks. An order `o` lands exactly on a bin only when

`o * revolutions` is an integer; otherwise it straddles two and both read

low. Measured on the run-up below, which happens to cover 79.994

revolutions:

============== ========== ============= =============

revolutions resolution amp at o=1.0 amp at o=3.5

============== ========== ============= =============

79 (default) 0.012658 0.999967 0.636961

78 (even) 0.012821 1.000009 0.999371

============== ========== ============= =============

That 0.637 is the classic two-bin scallop loss, and nothing raises: the peak

is at the right order and 36 % too small, with a second peak of almost equal

height one bin away (measured 0.6370 at order 3.4937 and 0.6353 at 3.5063).

Cropping to an even number of revolutions puts every half-integer order

on a bin. The default is the largest whole number available; pass

`revolutions` when the order you care about is fractional.

Returns a dict: `orders, magnitude (single-sided, 2/N`),

`peak_order, peak_amplitude, peak_orders / peak_amplitudes`,

`resolution_order, whole_revolutions, samples_per_rev`,

`mean_rpm, max_order`.

Measured, and this is the whole argument for the operator. A 4 s run-up from

600 to 1800 rpm at 5 kHz carrying exactly two shaft-locked components

(orders 1.0 and 3.5, unit amplitude) plus one fixed 400 Hz resonance, read

with `revolutions=78`:

========================== ===================== ====================

quantity ordinary spectrum order spectrum

========================== ===================== ====================

order-3.5 peak amplitude 0.070203 (of true 1) 0.999371 (of true 1)

its -3 dB width 66.50 Hz (= 3.33 ord) 0.00000 order

400 Hz resonance amplitude 1.0000, one bin 0.0517, over 26.7 ord

========================== ===================== ====================

The ordinary spectrum recovers 7 % of the shaft-locked component's

amplitude, because the energy is spread over 3.3 orders' worth of bins; the

order spectrum recovers 99.94 % of it in a single bin whose -3 dB width

is one bin. The 400 Hz resonance goes the other way — sharp in hertz,

smeared across 26.7 orders after resampling. That reversal is the

diagnostic, and it is why both spectra are worth computing: what stays sharp

under angular resampling turns with the shaft, and what stays sharp under

ordinary transformation does not.

Raises `ValueError: everything :func:angular_resample` refuses (in

particular the aliasing refusal), a `revolutions` larger than the record

actually contains, and a `max_order` above the angular Nyquist

`samples_per_rev/2`.

Detailed usage guide

acoustic_condition_monitoring family guide

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

acoustic_condition_monitoringpy -3.11 examples/acoustic_condition_monitoring.py

Ops the type connects to (they accept table as input)

istft

Same category (order)

angular_resample


*Provenance: acoustics.py — ACOUSTICS 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.