---
title: "signal-transforms — Mova code model"
description: "Mova code model of models/signal-transforms.groupant: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/models/signal-transforms.groupant/"
---
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# signal-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

- **kind:** groupant_group
- **status:** partial source bound group
- **bound sources:** 10
- **repository folder:** [`models/signal-transforms.groupant`](https://github.com/ElamurAI/mova-free/tree/main/models/signal-transforms.groupant)
- **repository commit:** `855da7bd4a7b`

> **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](#forward) |
| **ast** | not materialized |  |
| **composition** | partial source model | [composition](#composition) |
| **cost** | partial source model | [cost](#cost) |
| **descriptant** | partial source model | [epoch-memory](#epoch-memory) |
| **invariant** | partial source model | [invariant](#invariant) |
| **tests** | bounded executed | [wave26-evidence](#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](#behavior-complement) |
| `signal-transforms-reverse-reconstruction` | reverse_reconstruction | partial relational specification | [reverse-reconstruction](#reverse-reconstruction) |
| `signal-transforms-normalization_phase` | normalization_phase | partial relational specification | [normalization_phase](#normalization-phase) |
| `signal-transforms-extension_padding` | extension_padding | partial relational specification | [extension_padding](#extension-padding) |
| `signal-transforms-lossy_fiber` | lossy_fiber | partial relational specification | [lossy_fiber](#lossy-fiber) |
| `signal-transforms-polynomial_boundary` | polynomial_boundary | partial relational specification | [polynomial_boundary](#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](https://md.groupants.elamur.ai/free/en/mova/models/algorithm-library.groupant/#wave26-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](https://md.groupants.elamur.ai/free/en/mova/models/algorithm-library.groupant/#wave26-evidence) for scopes and limitations. These tagged APIs are not an invented serial pipeline.