synthesis op• Data kinds: none → signal (an op determined by its arguments alone — it takes no image or data input)
• Call: import acoustics; acoustics.synthesize_bearing_signal(rate=25600.0, duration=1.0, carrier_hz=3000.0, defect_hz=107.0, modulation=0.5, mode='am', damping=0.05, noise_sigma=0.0, seed=None) (or opsacoustics.get("synthesize_bearing_signal"))
A resonance amplitude-modulated at a known defect rate — the ground truth.
This is the whole reason envelope analysis exists, built forwards so the
answer is known before the measurement. A spall on a bearing race does not
radiate at the defect rate; it strikes a structure that rings at a much
higher resonance, once per defect passage. What reaches the microphone is a
carrier at the resonance, modulated at the defect rate, and the defect
rate itself is not present in the signal as a frequency component at all.
`mode="am"` gives the exactly analysable case,
`x(t) = (1 + m cos(2 pi f_d t)) sin(2 pi f_c t)`. Its analytic envelope is
exactly `1 + m cos(2 pi f_d t) for m < 1`, so the single-sided envelope
spectrum has a line of amplitude exactly m at `f_d` and nothing else.
Measured with `m = 0.5: :func:envelope_spectrum` returns a peak at
107.000000 Hz of amplitude 0.499677 (the 0.06 % shortfall is the band-pass
filter rolling off across the two sidebands, not the demodulation).
`mode="impulse"` gives the physically shaped case: an impulse train at
`f_d, each impulse ringing down as `exp(-2 pi zeta f_c t) sin(2 pi f_c
t)`. The envelope spectrum then shows f_d` and its harmonics, which
is what a real record looks like. Measured with `f_d = 107` Hz: the
envelope-spectrum peak is at 107.000000 Hz and the harmonics at 214 and
321 Hz carry 0.6542 and 0.4748 of the fundamental's amplitude.
In am mode the raw spectrum has nothing at `f_d`: measured, the raw
single-sided amplitude at 107 Hz is 4.3e-16, while the carrier reads
1.000000 and each sideband at 2893 and 3107 Hz reads 0.250000 — exactly
`m/2`, as amplitude modulation requires. In impulse mode the raw amplitude
at 107 Hz is 0.01165, not zero (an impulse train is not a pure product), but
still 18x below what the envelope spectrum recovers from the same record.
Raises `ValueError`: any non-real / non-finite / string / bool scalar,
`rate <= 0, duration <= 0, modulation outside [0, 1)` in am
mode (at `m >= 1 the envelope is |1 + m cos|`, which folds and puts
energy at `2 f_d — a rectified envelope, not the modulation), damping`
outside `(0, 1), a total length over :data:MAX_SAMPLES`, and — the one
that matters — **any requested frequency at or above Nyquist, including the
upper modulation sideband** `f_c + f_d`. An aliased carrier would come
back as a plausible signal at the wrong frequency with no error.
• acoustic_condition_monitoring family guide
• 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
signal as input)stft · envelope_spectrum · spectral_kurtosis · cepstrum · angular_resample · order_spectrum · octave_spectrum · weighting_response
synthesis)*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.