transform op• 資料種類:signal → table
• 呼叫:import acoustics; acoustics.stft(x, rate, win=256, hop=None, window='hann', nfft=None, scaling='none')(或 opsacoustics.get("stft"))
保留相位且可逆的短時傅立葉變換。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
:func:dsp.spectrogram returns magnitudes, which is all a display needs and
strictly less than an analysis needs: a magnitude spectrogram cannot be
turned back into a signal, so there is no path in :mod:dsp that filters or
modifies a signal in the time-frequency plane and comes back. This is that
path, and the test of it is that the round trip is exact.
Returns a dict (the transform plus everything :func:istft needs to undo
it):
`spectra`
complex128 `(n_freqs, n_frames)`, same orientation as
:func:dsp.spectrogram.
`freqs, times`
bin centre frequencies in Hz and frame start times in seconds. Frame
time 0.0 is the first *original* sample, so the leading pad does not
shift the time axis.
**`times[0]` is therefore negative**, and that is the consequence of
the sentence above rather than an error: the first frames start inside
the leading pad. Measured on 1.0 s at 16 kHz with `win=256, hop=128`,
`times[0] = -0.016000 and times[-1] = 1.000000`, a span 1.6 %
wider than the record. Do not hand `times[0] and times[-1]`
straight to a plot's time extent — the picture then claims a
time-frequency surface wider than the recording, whose outermost columns
are half-empty frames. Use `times[interior]`, whose first value is
exactly `0.000000`, for anything that has to line up with the signal.
`rate, win, hop, nfft, length, pad_left, scale`,
`scaling, window, window_values`
the geometry, kept so the inverse needs no arguments.
`nola_min`
the smallest value of the squared-window overlap sum over the original
samples. Reconstruction divides by this sum, so a value of zero means
some sample is not reconstructible; it is refused up front rather than
producing a hole.
`interior`
boolean mask over frames, true for the frames that lie **entirely inside
the original signal**. The transform pads by a full window at each end so
that inversion is exact, and the frames straddling that pad see part
zeros — they are correct as coefficients but they are not representative,
and any statistic averaged over *all* frames is therefore biased low.
Measured on 16384 samples of unit-variance white noise, win = 1024,
hop = 512: the `"density"` spectrum integrates to 0.9073 over all 35
frames and to 0.9933 over the 31 interior ones (the signal's own variance
is 0.9923). :func:spectral_kurtosis uses this mask for exactly that
reason — a half-empty frame looks impulsive.
Normalisation is explicit, because a windowed spectrum has no single
natural amplitude and a plausible-looking dB number is the usual result of
leaving it implicit. `scaling` selects a real factor applied to every
coefficient, recorded as `scale and divided out again by :func:istft`:
• `"none" (default) — the raw rfft` of the windowed frame.
• `"amplitude" — 2 / sum(w). A sinusoid of amplitude A` sitting on
a bin centre then reads `|Z| = A`. Measured on a 1 kHz, amplitude-0.7
tone at 16 kHz with a 256-sample periodic Hann, over the interior frames:
`|Z|` ranges 0.699999999999999 to 0.700000000000001.
DC and Nyquist read twice their amplitude under this convention (they are
not two-sided), which is the standard caveat and is not corrected for.
• `"density" — sqrt(2 / (rate * sum(w**2))), so |Z|**2` is a
single-sided power spectral density in units^2/Hz. Measured on 16384
samples of white noise at 16 kHz (win 1024, hop 512): the PSD integrates
to 0.9933 over the interior frames against the record's own variance
0.9923, and to 0.9073 if the pad frames are included — see `interior`.
Raises `ValueError`: non-1-D / non-finite / complex / masked input,
`rate <= 0, a string or bool rate, hop outside [1, win]`,
`nfft < win`, an unknown window, an all-zero window, a transform over
:data:MAX_STFT_ELEMENTS, and a window/hop pair whose squared overlap sum
touches zero (NOLA violated — the round trip would be silently lossy).
• acoustic_condition_monitoring 族使用指南
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者・年份)與用途見上面的族使用指南。
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
table 作為輸入)transform)*Provenance: acoustics.py — ACOUSTICS 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.