spectral op• Data kinds: signal → table
• Call: import fullseye as fs; fs.ledger.hilbert_analytic(x, fs: 'float' = 1.0) -> 'dict' (to call the implementation directly, import mathspectral; mathspectral.hilbert_analytic(x, fs: 'float' = 1.0) -> 'dict'; from the registry, opsmath.get("hilbert_analytic"))
> This operator's description has not been translated yet. The original text follows as it is.
解析信号 z = x + i·H[x] (FFT で負の周波数を消す)と、そこから読む振幅・瞬時位相・瞬時周波数。
Args:
x: 実の 1-D 信号。
fs: 標本化周波数(瞬時周波数の単位を決める)。
Returns:
`analytic 複素の解析信号、amplitude |z|(包絡線)、phase` 連続につないだ位相 [rad]、
`frequency` 瞬時周波数 = 位相の時間微分 / 2π(中心差分、長さは x と同じ)。
門: cos → sin(Hilbert 変換の定義)、線形チャープの瞬時周波数が f0 + k·t、Bedrosian の定理(包絡線が
搬送波より低い帯域なら AM 信号の振幅がそのまま戻る)。端は周期の仮定で乱れる(信号を窓で絞ると減る)。
Every mathops op validates its input before computing (nothing slips through silently):
• **complex input raises ValueError** — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• **masked arrays with masked elements raise ValueError** — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• **NaN/Inf raises ValueError on every input** (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• 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.
• spectral_tour — py -3.11 examples/spectral_tour.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
spectral)lomb_scargle · ula_snapshots · music_doa · esprit_doa · n_sources_mdl
*Provenance: mathspectral.py — MATH 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.