Elamur Groupantssignal-transforms
The groupant beside models/signal-transforms.groupant in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial source model | forward |
| ast | not materialized | |
| composition | partial source model | composition |
| cost | partial source model | cost |
| descriptant | partial source model | epoch-memory |
| invariant | partial source model | invariant |
| tests | bounded executed | wave26-evidence |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
signal-transforms-behavior-complement | behavior_complement | partial relational specification | behavior-complement |
signal-transforms-reverse-reconstruction | reverse_reconstruction | partial relational specification | reverse-reconstruction |
signal-transforms-normalization_phase | normalization_phase | partial relational specification | normalization_phase |
signal-transforms-extension_padding | extension_padding | partial relational specification | extension_padding |
signal-transforms-lossy_fiber | lossy_fiber | partial relational specification | lossy_fiber |
signal-transforms-polynomial_boundary | polynomial_boundary | partial relational specification | polynomial_boundary |
Model text
model
signal-transforms
forward
Tagged real/complex signal maps: DCT coefficients, Haar multiscale coefficients, arbitrary-length Bluestein DFT, Goertzel frequency observations and Savitzky-Golay local polynomial smoothing. Sample coordinates and normalizations are part of the result type. Orthonormal DCT/Haar: y=Qx,Q^TQ=I,x=Q^Ty with full coefficients in real arithmetic. Goertzel bin k is X_k=sum_j x_j exp(-2πijk/n) under matching DFT convention; Bluestein computes full DFT by chirp convolution.
invariant
Length, finite arithmetic, padding, frequency indexing, coefficient normalization, window and boundary conventions remain explicit. A spectral bin, full invertible transform and smoothed signal discard different information.
cost
DCT direct dense work and Haar linear pair stages follow their kernels. Bluestein chooses a convolution length and pays FFT/padding storage; Goertzel costs signal length per queried bin; Savitzky-Golay includes coefficient preparation plus window work. Repeated-bin comparisons include the queried-bin count; no blanket FFT or smoothing gain is inferred.
composition
DCT-to-DFT comparisons require the exact even-extension and scale convention. Goertzel agrees with a chosen DFT bin only under matching phase/sign/frequency conventions, including endpoint bins. Haar reconstruction needs retained detail coefficients and compatible length. Savitzky-Golay polynomial preservation applies only to degree/window/boundary rules actually admitted; smoothing is not a generally invertible preprocessing step.
limitations
Successful allocations and each leaf's finite domain/error precedence. These are tagged relations, not automatic production adoption. Floating residuals are not solution-error guarantees. No generic 1/2/5/10% composition-wide profile; finite evidence remains separate from analytical claims.
epoch-memory
Wave26, 2026-10-30. Tagged library tools; no automatic training adoption, source-volume quality claim or generic numerical profile.
checks
["cargo test -p mova-algorithms discrete_cosine_transform::tests","cargo test -p mova-algorithms haar_wavelet::tests","cargo test -p mova-algorithms bluestein_fft::tests","cargo test -p mova-algorithms goertzel::tests","cargo test -p mova-algorithms savitzky_golay::tests"]
wave26-executed-checks
signal-transforms: wave26 checks
20 source-local test declarations across five modules. Every module has a compiled failing production mutation followed by exact restoration. The final whole library passed 877 checks twice debug and twice release. See integrated evidence for scopes and limitations. These tagged APIs are not an invented serial pipeline.
catalog
Typed family relations
behavior-complement
Type: behavior_complement.
Exclude wrong normalization/phase/length, replacing complex bin by magnitude without projection, or reconstruction after dropping Haar details. Savitzky-Golay polynomial reproduction requires admitted degree/window/boundary conventions; rounding is separate.
reverse-reconstruction
Type: reverse_reconstruction.
Full exact orthonormal y uniquely reconstructs x=Q^Ty at fixed convention. Goertzel bin z has fiber {x:sum_j x_j exp(-2πijk/n)=z}, generally nontrivial nullspace. Smoothing admits {x:Sx=y}; rank determines uniqueness. Rounded outputs have rounding-compatible fibers.
normalization_phase
Type: normalization_phase.
Transform comparisons must preserve Fourier sign, frequency units and normalization; raw coefficient equality across conventions is excluded.
extension_padding
Type: extension_padding.
DCT even extension and Bluestein convolution padding have different purposes; padding must not alter interpreted sample count.
lossy_fiber
Type: lossy_fiber.
A single Goertzel bin, omitted Haar details or smoothed output admits many input signals; no unique inverse is claimed.
polynomial_boundary
Type: polynomial_boundary.
Polynomial reproduction depends on degree and boundary window semantics; interior identities do not justify edge extrapolation.
wave26-evidence
signal-transforms: wave26 checks
20 source-local test declarations across five modules. Every module has a compiled failing production mutation followed by exact restoration. The final whole library passed 877 checks twice debug and twice release. See integrated evidence for scopes and limitations. These tagged APIs are not an invented serial pipeline.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/models/signal-transforms.groupant/