signal op• Data kinds: signal → pairs
• Call: import fullseye as fs; fs.ledger.spectrum(x, rate=1.0) (to call the implementation directly, import dsp; dsp.spectrum(x, rate=1.0); from the registry, ops1d.get("spectrum"))
• Return value through the ledger: fullseye.ledger.spectrum(...) returns only the declared out type pairs (the underlying function also returns auxiliary values). When you need what was dropped, use fullseye.ledger.spectrum.raw(...) or call dsp.spectrum directly.
Raw one-sided magnitude spectrum -> (freqs, magnitude) (np.fft.rfft).
Scaling convention — read this before comparing any number. *One-sided* describes the frequency axis, not the amplitude axis. rfft keeps only the non-negative frequencies, so freqs runs from 0 to rate/2 in len(x)//2 + 1 bins — but magnitude is the unnormalised |rfft(x)|. It is *not* an amplitude and it grows with len(x): the same tone recorded twice as long comes back twice as tall. Nothing here divides by N; the caller does, and the exact factor depends on the bin::
freqs, mag = spectrum(x, rate)
amp = mag * (2.0 / len(x)) # one-sided amplitude, bins 1 .. N/2-1
amp[0] /= 2.0 # DC has no mirror twin -> no factor 2
if len(x) % 2 == 0:
amp[-1] /= 2.0 # nor does the Nyquist bin of an even N
The factor is 2/N and not 1/N because a real sinusoid of amplitude A splits its energy over a positive and a negative frequency; rfft discards the negative half, so the surviving bin holds A*N/2. DC and (for even N) Nyquist are their own mirror image and are *not* doubled — applying 2/N to them reports twice the true level.
Measured, so the convention can be checked rather than assumed. A unit sine at a bin centre (rate = 25600 Hz, N = 25600, 3000 Hz, amplitude exactly 1.0): the returned mag at 3000 Hz is 12799.999999999998 (= N/2), and mag * 2/N is 0.9999999999999999. A constant signal of value 1.0 with N = 1024: mag[0] = 1024.0, so mag[0] * 1/N is exactly 1.0 while mag[0] * 2/N would claim 2.0. Likewise cos(pi n) (amplitude 1.0 at Nyquist, N = 1024): mag[-1] = 1024.0, * 1/N = 1.0, * 2/N = 2.0.
Everything scale-*invariant* — where the peak is, the spectral centroid, the bandwidth, a ratio between two bins — is unaffected by the convention, which is why signal_features can build on this directly. Everything absolute (an amplitude in the signal's own units, a dB level) needs the division above. acoustics.envelope_spectrum and acoustics.order_spectrum already return calibrated one-sided amplitudes (they apply their own 2/N internally) — do not apply the factor twice when comparing their output with this one.
• 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.
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
• poc_bearing_diagnosis — py -3.11 examples/poc_bearing_diagnosis.py
• poc_gear_tooth_metrology — py -3.11 examples/poc_gear_tooth_metrology.py
• poc_machine_condition_fusion — py -3.11 examples/poc_machine_condition_fusion.py
• poc_pipe_wall_loss — py -3.11 examples/poc_pipe_wall_loss.py
• poc_recycling_sorting — py -3.11 examples/poc_recycling_sorting.py
• poc_web_roll_periodicity — py -3.11 examples/poc_web_roll_periodicity.py
pairs 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.