signal op• Datenarten: signal → pairs
• Aufruf: import fullseye as fs; fs.ledger.spectrum(x, rate=1.0) (die Implementierung direkt: import dsp; dsp.spectrum(x, rate=1.0); aus dem Register: ops1d.get("spectrum"))
• Rückgabewert über das Register: fullseye.ledger.spectrum(...) liefert **nur den Wert des deklarierten Out-Typs pairs** (die zugrunde liegende Funktion gibt zusätzlich Hilfsinformationen zurück). Wird das Verworfene gebraucht, nutze fullseye.ledger.spectrum.raw(...) oder rufe dsp.spectrum direkt auf.
> Für diesen Operator gibt es noch keine Übersetzung. Es folgt der Originaltext unverändert.
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 :func:signal_features can build on this directly. Everything
absolute (an amplitude in the signal's own units, a dB level) needs the
division above. :func:acoustics.envelope_spectrum and
:func: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.
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• 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 als Eingabe)—
signal)lowpass · highpass · bandpass · envelope · rms · local_std · quantize · companding_mu_law
*Provenance: dsp.py — ONED Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.