transform op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.wavelet_filters(order: 'int' = 2) -> 'dict' (to call the implementation directly, import mathtransforms; mathtransforms.wavelet_filters(order: 'int' = 2) -> 'dict'; from the registry, opsmath.get("wavelet_filters"))
Builds the filters of the Daubechies orthonormal wavelet dbN by the textbook construction (spectral factorization).
|H(ω)|² = cos^{2N}(ω/2)·P(sin²(ω/2)), P(y) = Σ_{k<N} C(N−1+k, k) y^k (Daubechies 1988). From the roots of P, the zeros inside the unit circle are chosen and multiplied with (1 + z⁻¹)^N. No table is copied, so there are no transcription errors from loss of significant digits (the gate checks the values).
Returns:
lowpass h (length 2N, sum √2), highpass g[n] = (−1)^n h[2N−1−n], order,
vanishing_moments = N (polynomials up to degree N−1 are cancelled in the detail coefficients). order=1 is Haar.
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.