transform op• Data kinds: signal × signal → table
• Call: import fullseye as fs; fs.ledger.tf_bilinear(num, den, fs: 'float' = 1.0, *, prewarp_hz: 'float | None' = None) -> 'dict' (to call the implementation directly, import mathtransforms; mathtransforms.tf_bilinear(num, den, fs: 'float' = 1.0, *, prewarp_hz: 'float | None' = None) -> 'dict'; from the registry, opsmath.get("tf_bilinear"))
> This operator's description has not been translated yet. The original text follows as it is.
Tustin(双一次)変換 s = K (z − 1)/(z + 1) で連続系を離散系に写す。
K = 2·fs(素の Tustin)か、`prewarp_hz` を与えると K = ω₀ / tan(ω₀ / (2 fs))
(その周波数で連続系と離散系の応答が厳密に一致する。それ以外の周波数は tan で歪む)。
返り値の係数は z の降べき(`np.polyval(num_z, z)`)。安定な連続系は安定な離散系になる(左半面 → 単位円内)。
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.
• (none yet)
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
transform)abel_transform · abel_inverse · abel_inverse_image · abel_revolve · hankel_transform · tf_poles_zeros · tf_freq_response · tf_impulse_response
*Provenance: mathtransforms.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.