wdm-transform

wdm-transform provides Wilson-Daubechies-Meyer (WDM) transforms and an opt-in orthogonalized modified-Gaussian Wilson (WDG) window for sampled one-dimensional signals. Both use the same package, objects, and coefficient layout.

The public API centers on three objects:

• TimeSeries
• FrequencySeries
• WDM

Choose a window

Use Meyer for compact frequency support and the lowest transform cost; try Gaussian when tighter time localization matters for transients or data gaps. Gaussian trades that localization for wider frequency mixing. See Choosing a window for the comparison figure, parameter guidance and Noah Pearson et al.'s paper.

import numpy as np
from wdm_transform import TimeSeries

data = np.random.default_rng(42).normal(size=8192)
ts = TimeSeries(data, dt=5.0)
meyer = ts.to_wdm(nt=256, window="meyer")
gaussian = ts.to_wdm(nt=256, window="gaussian")
recovered = gaussian.to_time_series()  # retains the originating window

Omitting window keeps the original Meyer defaults, a=1/3, d=1. Gaussian uses nu=0.5 and support=min(16,nf) by default; support counts half-band spacings retained on each side of a frequency-window center. It controls finite-tail reconstruction error, rather than the number of signal samples. The currently validated shape range is 0.3 <= nu <= 0.8; small nf can limit accuracy. Set nu and support explicitly when needed.

Both results have real coefficients shaped (batch, nt, nf+1). WDM records window, nu, and effective support as keyword-only metadata and passes them to every inverse. Changing basis requires a new transform; changing metadata does not convert coefficients. Gaussian rejects nondefault a/d, and Meyer rejects explicit nu/support.

Gaussian full transforms support NumPy, JAX, and the shared CuPy implementation; GPU correctness requires a CuPy-capable machine. Compact subband APIs accept the same window options; Gaussian uses wider frequency margins. The existing wdm_noise_variance channel-PSD approximation is not a calibrated WDG colored-noise covariance model. The runnable docs/examples/gaussian_comparison.py example generates the guide's figure.

Installation

pip install wdm-transform

Optional JAX support:

pip install "wdm-transform[jax]"

If you prefer uv:

uv add wdm-transform

Useful repository commands from the project root:

# make a new venv for the repo
uv venv

# install local dev dependencies
uv sync --extra dev

# include docs dependencies too
uv sync --extra dev --extra docs

# run the walkthrough example
uv run python docs/examples/wdm_walkthrough.py

# run the test suite
uv run pytest

# build the docs
uv run mkdocs build

# serve the docs locally
uv run mkdocs serve

# run the benchmark CLI
uv run wdm_transform_benchmarking --backends numpy jax --pow2 12 22

# compare window families with synchronized timings and reconstruction errors
uv run wdm_transform_window_benchmark --backends numpy jax --runs 7 --outdir test_output/wdg_benchmarks

# refresh the checked-in benchmark snapshot used in the docs
uv run python docs/examples/generate_benchmark_plot.py --backends numpy jax

Documentation and source live at:

• https://github.com/pywavelet/wdm_transform
• https://github.com/pywavelet/wdm_transform/tree/main/docs