Scattering Texture Generator — Wavelet-Scattering Texture Resynthesis

What this does

Scattering Texture Generator analyses a selected Sound with a one-dimensional Morlet wavelet-scattering representation and constructs a new waveform realization whose selected scattering statistics approach a source-derived or transformed target. Instead of copying the original waveform, the system preserves higher-level relationships such as spectral-band energy, coarse envelope shape, and multiscale modulation behavior.

Key Features:

• Orders 0, 1, and 2 — coarse energy envelope, wavelet-band structure, and second-order modulation.
• Normalized second-order matching — order 2 is matched as S2 / S1, so modulation depth is not simply another measure of spectral energy.
• 6 named creative presets + Custom — from Spectral Skeleton to Radical Texture.
• Target transformation — smoothing, spectral shifts, modulation-rate shifts, dynamic compression/expansion, sparsification, and structured perturbation.
• Spectral randomization — move carrier magnitude from the source spectrum toward a smoothed pitch-reduced spectral envelope.
• Calibrated direct synthesis — builds the waveform from the target before optional optimization.
• Optional L-BFGS refinement — Standard and High modes further reduce scattering-domain mismatch.
• Parallel segmented processing — long sounds are processed in independent overlapping segments and joined with equal-power crossfades.
• Reproducible variation — reuse a seed to recreate the same stochastic realization.
• Explanatory Praat Picture visualisation — source, multiscale structure, second-order modulation, target constraints, matching, and output.
• CPU-only and offline — no neural model, training, cloud service, API, GPU, or downloaded model weights.

Quick start

1. Select exactly one Sound object in Praat.
2. Run Scattering_Texture_Generator.praat.
3. For a first run, leave Preset = Custom, Texture scale = Medium, and Frequency detail = Medium.
4. Use the default preservation weights: Global envelope 40%, Spectral structure 60%, Temporal modulation 100%.
5. Use Texture transformation to determine how strongly the scattering target itself is altered.
6. Use Spectral randomization to progressively remove fine spectral / pitch identity from the carriers.
7. Start with Preview for a fast direct-synthesis result. Use Standard or High when you want iterative refinement.
8. Keep Draw visualization enabled to inspect source, target, achieved scattering structure, and loss behavior.

How it works

1. Praat exports a mono analysis signal

The selected Sound is preserved in the Object list. If it has more than one channel, Praat converts a temporary copy to mono for analysis and synthesis, applies a protective pre-scale only when required for 24-bit WAV export, and sends the temporary WAV to the Python backend.

2. Kymatio Morlet filters define the scattering representation

The Python engine uses Kymatio's one-dimensional Morlet filter bank. The forward scattering path is implemented in NumPy with Fourier-domain filtering, dyadic subsampling, modulus, and low-pass averaging. Orders 1 and 2 follow the Kymatio scattering structure; order 0 uses an envelope form appropriate for audio.

3. The source representation becomes a texture target

The source coefficients are moved into a log-domain target representation. A preset may apply its own structural operations, while Texture transformation scales a second group of target operations. These transformations act on the representation itself rather than functioning as a dry/wet control.

4. A new waveform is built from the target

For every first-order band, the engine creates a phase-randomized carrier. Its magnitude spectrum ranges from the source's detailed spectrum toward a smoothed pitch-reduced envelope according to Spectral randomization. Time-varying first-order envelopes and second-order Morlet-band modulation signals are then imposed on those carriers.

5. Calibration and optional refinement

The direct-synthesis stage repeatedly re-analyses the new waveform and corrects first-order levels and second-order modulation depths. Standard and High modes then use an analytic scattering gradient and L-BFGS to reduce a weighted log-domain mismatch.

Scattering orders — Musical interpretation

6 Presets + Custom

Controls

Reconstruction quality

Visualisation

When Draw visualization is enabled, the script produces a Praat Picture display organised as a five-stage explanation of the transformation:

Technical behavior

• Processes exactly one selected Sound and never modifies the original object.
• Converts multichannel input to a temporary mono analysis copy; the generated result is mono.
• Exports a temporary 24-bit WAV, with protective pre-scaling only when necessary.
• Uses Kymatio's Morlet filter-bank definitions but performs scattering and its analytic adjoint in NumPy.
• Order 0 uses |x| * phi_J because the ordinary low-passed audio waveform is near zero for DC-free audio.
• Order 2 is matched in normalized S2/S1 form so temporal-modulation preservation does not simply re-impose spectral-band level.
• Coefficient-family losses are computed in the log domain and normalized by coefficient count.
• Direct synthesis creates first-order carriers and second-order modulation sources using the same Morlet families used by the analysis.
• Long sounds are segmented with context margins and reassembled with equal-power crossfades.
• Segment jobs can run in parallel worker processes; worker FFTs use a single thread to avoid CPU oversubscription.
• If multiprocessing cannot start, the backend falls back to a single process.
• Silent input returns silence of identical duration.
• Output sample count and sample rate are checked against the source before the Sound is accepted.
• Output RMS is matched to the source and peak protection attenuates only when required.
• Temporary files are cleaned after processing.
• The Info window reports the seed, order weights, J, averaging scale, Q values, path counts, modulation-rate range, working rate, band limit, segmentation, calibration, refinement, target operations, loss reduction, and warnings.

Requirements & installation

Limitations

• Not an exact reconstruction: scattering is used as a texture constraint, so the output is intentionally a new realization rather than a waveform copy.
• Mono output: multichannel source material is mixed to mono before scattering analysis and resynthesis.
• Pitch identity is not explicitly preserved: the method can retain broad spectral structure while exact harmonic phase and fine pitch identity are deliberately released.
• Spectral randomization does not disable phase randomization: the control changes the carrier magnitude spectrum; random carrier phase is used throughout the direct-synthesis process.
• Preset operations can be active at Transformation 0: some named presets intentionally contain always-on structural operations.
• Quality changes internal bandwidth: Preview, Standard, and High use different working-rate caps in addition to different refinement depths.
• CPU cost can be substantial: fine frequency detail, broad texture scale, long sounds, and High refinement require more computation and memory.
• Minimum source duration: the Praat frontend rejects Sounds shorter than 20 ms.

Outputs

The script creates a new mono Sound. In Custom mode the normal name is:

<original-name>_ScatteringTexture

Named presets use concise output tags, for example:

<original-name>_SpectralSkeleton
<original-name>_TemporalTexture
<original-name>_ModulationGhost
<original-name>_StructureWithoutIdentity
<original-name>_SecondOrderReconstruction
<original-name>_RadicalTexture

The output preserves the source duration, start time, and sample rate. The original Sound remains unchanged.

Applications

Texture-preserving re-synthesis

Use case: create a new realization of a sound while retaining broad spectrum, envelope behavior, or modulation statistics rather than its exact waveform.

Starting point: Custom, Medium scale, Medium detail, moderate order-1 weight and high order-2 weight.

Extract a spectral skeleton

Use case: retain broad timbral organisation but allow attacks, tremolo, and local temporal motion to diverge.

Starting point: Spectral Skeleton.

Preserve motion while changing identity

Use case: keep pulsation, articulation density, or modulation behavior while suppressing literal timbral similarity.

Starting point: Temporal Texture or Modulation Ghost.

Second-order experimental resynthesis

Use case: foreground what wavelet scattering adds beyond first-order CWT structure by making modulation constraints dominant.

Starting point: Second-Order Reconstruction.

Generate structurally related but strongly transformed material

Use case: create new material for electroacoustic composition in which the source's multiscale organisation remains perceptible while spectral and modulation coordinates are actively displaced.

Starting point: Radical Texture with increased Texture transformation and Spectral randomization.